Quadratics

Problem 2201

Find $f(-4)$ for the function $f(x)=x^{2}-2x-6$ .

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Problem 2202

Find $c$ if the average value of $f(x)=x^{2}+c x$ over $[0,7]$ equals 4. Enter your answer as a decimal.

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Problem 2203

Video
Solve for s. $s^{2}+23 s+22=0$
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $s=$ $\square$ Submit

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Problem 2204

$8x^2 + 112px + 8y^2 - 64py = -448p^2$
In the $xy$ -plane, the graph of the given equation is a circle. The length of the radius of the circle is $np$ , where $n$ and $p$ are positive constants. What is the value of $n$ ?
Answer Preview:

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Problem 2205

What are the roots of the equation $x^{2}-10 x+26=0$ in simplest $a+b i$ form?
Answer
Additional Solution No Solution

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Problem 2206

Year 10 (B) Mathematics
Question 2 (a) Factorise $y=10+3 x-x^{2}$ . (b) Hence sketch the graph of $y=10+3 x-x^{2}$ . (c) Is the graph concave up or down? (d) What is the axis of symmetry? (e) Find the coordinates of the vertex. (f) What is the maximum value of the parabola?

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Problem 2207

For the function $f(x)=3 x^{2}-4$ , which domain restriction makes $f(x)$ invertible? Select from $(0, \infty)$ , $(-1, \infty)$ , or $(-4, \infty)$ . What is $f^{-1}$ ?

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Problem 2208

Find the solutions for $x^2 + 3.5x - 2 = 0$ . Options: A. 0.5 B. -0.5 C. 4 D. -4 E. $\frac{-7+\sqrt{17}}{2}$ F. $\frac{-7-\sqrt{17}}{2}$ G. $\frac{7+\sqrt{17}}{2}$ H. $\frac{7-\sqrt{17}}{2}$ .

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Problem 2209

Select the true equalities for the function $g(x)=x^{2}+3x-1$ : A. $g(-4)=3$ , B. $g(0)=2$ , C. $g(1)=3$ , D. $g(2)=9$ , E. $g(3)=14$ .

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Problem 2210

Find the domain restriction for $f(x)=3x^{2}-4$ to make it invertible, and identify $f^{-1}(x)$ . Options: A, B, C, D.

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Problem 2211

Find real solutions using the square root property for: $3 n^{2}+240=0$ and $4 s^{2}-288=0$ . Provide exact answers.

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Problem 2212

Solve for $x$ using the square root property: $3 x^{2}+73=94$ . Enter answers as a list, e.g., $4, -\frac{2}{3}$ .

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Problem 2213

Solve the equation $p^{2}-11p+28=0$ . Enter your integer or fraction answers separated by commas.

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Problem 2214

Solve the equation: $z^{2}=19 z-84$ . Find $z=$ . If multiple solutions, separate with a comma.

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Problem 2215

Rewrite $x^{2}-8 x-4=0$ as $(x-p)^{2}=q$ .

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Problem 2216

Solve the equation $z^{2}+14z-49=6$ by completing the square. Find the value to add, the equation form, and solutions.

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Problem 2217

Solve the equation using the quadratic formula: $3 r^{2}-r-1=0$ . List the solutions, separated by commas. $r=$

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Problem 2218

Find the number and type of solutions for $5x^{2} + 5x - 2 = 0$ . Options: rational, imaginary, repeated, or irrational.

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Problem 2219

If the discriminant of a quadratic equation is 4, what can you say about its solutions?

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Problem 2220

If the discriminant of a quadratic equation is -2, what can you say about the equation's roots?

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Problem 2221

In Exercises 1-8, describe how the graph of $y=x^{2}$ can be transformed to the graph of the given equation.
1. $y=x^{2}-3$
2. $y=x^{2}+5.2$
3. $y=(x+4)^{2}$
4. $y=(x-3)^{2}$
5. $y=(100-x)^{2}$
6. $y=x^{2}-100$
7. $y=(x-1)^{2}+3$
8. $y=(x+50)^{2}-279$

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Problem 2222

Solve $6x^2 + 9x = 0$
$x =$ (Separate answers by a comma. Write answers as integers or reduced fractions.) Question Help: Video

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Problem 2223

4. [Maximum mark: 4] Solve for n: $\binom{n}{2} - 2n = 20$

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Problem 2224

Find the minimum $y$ -value on the graph of $y = 8x^2 - 32x + 37$ .
The minimum $y$ -value is $\boxed{\phantom{00}}$ .

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Problem 2225

$y = 3x^2 + 90x + 50$

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Problem 2226

10. Choose ONE of the following questions.
A bus company has 4000 passengers daily, each paying a fare of $\$2$ . For each 15 cent increase in price, the company estimates it will lose 40 passengers. If the company needs to take in $\$10,450$ per day to stay in business, what fare should be charged?

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Problem 2227

Question Watch Video Show Examples
Ava launches a toy rocket from a platform. The height of the rocket in feet is given by $h(t)=-16 t^{2}+24 t+112$ where $t$ represents the time in seconds after launch. After how many seconds does the rocket hit the ground?
Answer Attempt 1 out of 3 $\qquad$ seconds Submit Answer

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Problem 2228

Question
Solve for all values of $x$ by factoring. $x^{2}+x-16=x$
Answer Attempt 1 out of 3

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Problem 2229

Solve the equation $2 x^{2}-19 x+2=-10 x$ to the nearest tenth.
Answer Attempt 1 out of 3 (ค) Additional Solution $\Theta$ No Solution

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Problem 2230

Solve the following inequality algebraically. $-3 x^{2}+5 x>-3 x-3$
Answer Attempt 1 out of 3 $\square$

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Problem 2231

Find real numbers a, b, and c so that the graph of the function $y = ax^2 + bx + c$ contains the points $(-1,6)$ , $(2,7)$ , and $(0,3)$ .
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution is $a =$ , $b =$ , and $c =$ . (Type integers or simplified fractions.)
B. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(a,b,c) | a =$ , $b =$ , c any real number\}. (Simplify your answers. Type expressions using c as the variable as needed.)
C. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(a,b,c) | a =$ , b any real number, c any real number\}. (Simplify your answer. Type an expression using b and c as the variables as needed.)
D. There is no solution.

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Problem 2232

Solve by completing the square: $z^{2}=12 z+1$

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Problem 2233

$x^2 + y^2 - 6x + 8y + 16 = 0$

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Problem 2234

14. The graph of which function has the same axis of symmetry as the graph of $y=2 x^{2}-8 x+3$ ? Explain your reasoning. A. $y=-4 x^{2}+16 x-5$ B. $y=2 x^{2}+8 x+7$ C. $y=3 x^{2}-6 x+7$ D. $y=-6 x^{2}+10 x-1$

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Problem 2235

$x^{2}-14 x+49$ $a^{2}+28 a+19 b$
For \#30 \& 31, (a) Write the third term for "Completing the Square" of the perfect square trinomial. (b) Write the perfect square trinomial as a binomial squared. 30) $\mathrm{x}^{2}+18 \mathrm{x}+$ $\qquad$ 31) $a^{2}+11 a+$ $\qquad$

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Problem 2236

15. $(2 x-7)(x+5)=0$

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Problem 2237

The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area ( $A$ ) of the room? - $A=x(x+5)$ $A=x+(x+5)$ $A=5 x$ $A=2 x+2(x+5)$

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Problem 2238

tion list restion 14 vestion 15
Find the zerrs of the function aloworracally. $f(x)=3 x^{2}-x+2$
The zeros are $\square$ . (Sinclly your answer: Type an exact answer, using radicals and ias needed. Use inte

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Problem 2239

$x^2 + 8x + 12 = 0$

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Problem 2240

Solve the equation $x^{2}+8 x+17=0$ and express solutions as $a+b i$ .

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Problem 2241

Solve for real values of $x$ in the equation $(x+9)^{2}-7(x+9)-18=0$ .

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Problem 2242

Bianca's towel is 16 ft by 28 ft. Use the difference of two squares to find its area. Which expression is correct? $28^{2}-16^{2}$

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Problem 2243

Given $f(x)=5 x^{2}-x+2$ , find $f(-a)$ , $f(a+1)$ , $2 f(a)$ , $f(2 a)$ , $f(a^{2})$ , $[f(a)]^{2}$ , and $f(a+h)$ .

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Problem 2244

Factor and solve $4 x^{2}+12 x+5=-4$ . Find the values of $x$ .

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Problem 2245

Find the max or min of the function: $f(x)=-x^{2}-3x+3$ .

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Problem 2246

Find the roots of the equation $2x^{2}-13x+20=0$ .

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Problem 2247

Solve the inequality $f(x) \geq 0$ for $f(x)=(x+4)(x-2)^{2}$ using its graph. Answer in interval notation: $\square$ .

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Problem 2248

Solve the equation $2x^{2}+7x+6=0$ for the variable $x$ .

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Problem 2249

Factor and solve the equation $4 a^{2}+11 a-20=0$ . Find values for $a$ :
$a=$ or $a=$

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Problem 2250

Solve the equation $-6 x^{2}-20 x-16=0$ for $x$ and simplify your answers. If multiple solutions, separate with a comma.

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Problem 2251

Solve for real $x$ in the equation $x^{2}-10x+23=23$ by completing the square. Find $x_{1}$ and $x_{2}$ with $x_{1}<x_{2}$ .

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Problem 2252

Factor and solve the equation $4 a^{2}+11 a-20=0$ . Find $a=$ or $a=$ .

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Problem 2253

Solve the following quadratic equation using the quadratic formula. $-4y^2 - 3y + 4 = 0$

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Problem 2254

aph of a parabola is given on the right. Match the graph to its equation.

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Problem 2255

Identify the equation without completing the squares. $8 x^{2}+5 y^{2}-4 x+7 y=0$
Choose the conic that matches the given equation. A. Hyperbola B. Ellipse C. Parabola D. The equation does not represent a conic. E. Circle

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Problem 2256

parabola is given on the right. Match the ation.
Choose the correct equation below. A. $(y+4)^{2}=4(x+1)$ B. $(y+4)^{2}=-4(x+1)$ C. $(x-1)^{2}=4(y-4)$ D. $(y-4)^{2}=-4(x-1)$ E. $(y-4)^{2}=4(x-1)$ F. $(x-1)^{2}=-4(y-4)$ G. $(x+1)^{2}=-4(y+4)$ H. $(x+1)^{2}=4(y+4)$

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Problem 2257

22 Solve the following quadratic equations by square roots. Write all answers in simplest form.
$3x^2 - 108 = 0$
$x^2 = 36$
Solution(s):

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Problem 2258

$9x^2 - 16 = 0$ $x^2 =$ Solution(s):

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Problem 2259

Solve each quadratic.
1. $3 \cot^2{x} - 3 \cot{x} = 1$

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Problem 2260

Solve the equation using the quadratic formula. $2 x^{2}-3 x=-5$
The solution set is $\square$ \} (Simplify your answer. Type an exact answer using radicals and $i$ as needed. Use answers as needed.)

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Problem 2261

11 12 13 14 15 16 17 18
For which value of $m$ does the graph of $y=18 x^{2}+m x+2$ have exactly one $x$ -intercept? 0 9 12 16 Mark this and return Save and Exit Next

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Problem 2262

Solve $x^{2}-16 x+60=-12$ by completing the steps. First, subtract $\square$ from each side of the equation. DONE

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Problem 2263

$b = \frac{a+x^2}{3}$ Make x the subject.

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Problem 2264

Solve the system by the addition method. $\left\{\begin{array}{l} x^{2}-3 y^{2}=-11 \\ 4 x^{2}+y^{2}=8 \end{array}\right.$
The solution set is $\square$ \}. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

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Problem 2265

Solve the inequality and graph the solution on the real number line. $(x-4)^{2} \geq 1$

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Problem 2266

Solve the system by the addition method. $\begin{cases} x^2 - 4y^2 = -32 \\ 2x^2 + y^2 = 17 \end{cases}$ The solution set is $\{\}$ . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

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Problem 2267

Solve the system by the method of your choice.
$x^2 + 2y^2 = 729$ $x + y = 27$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is $\{\}$ . (Type an ordered pair, using integers or simplified fractions for the coordinates. Use a comma to separate answers as needed.)
B. There is no solution.

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Problem 2268

Using the graph, determine the coordinates of the vertex of the parabola.
Answer Attempt 1 out of 2
Answer type Submit Answer
Two points One point One equation

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Problem 2269

Question
Solve the equation for all real solutions in simplest form. $4 y^{2}-14 y+9=0$

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Problem 2270

Du hast die Funktion $f(x)=-0,5 x^{2}+5,5$ . Du musst zeigen, dass der Punkt A(2|3,5) auf der Parabel f liegt. Dann begründen, dass deshalb auch B(-2|3,5) auf der Parabel f liegt. Dann den Umfang vom Rechteck ABCD berechnen und noch so ein Rechteck mit A2(1|5) zeichnen. Dann sollst du begründen, dass man mit 22x+2(-0,5x² $+5,5)$ jedes Rechteck unter der Parabel f berechnen kann, wobei x die xKoordinate vom Punkt A ist. Dann durch Termumformung zeigen, dass $2 2 x+2\left(-0,5 x^{2}+5,5\right)=-$ $x^{2}+4 x+11$ ist. Und noch berechnen für welches $x \quad-x^{2}+4 x+11=14,75$ ist und erklären was das im Kontext bedeutet. Zuletzt noch den Scheitelpunkt $u(x)=-x^{2}+4 x+11$ berechnen und erklären was

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Problem 2271

7. The height above the ground of a bungee jumper is modelled by the quadratic function $h(t) = -5(t - 0.3)^2 + 110$ , where height, $h(t)$ , is in metres and time, $t$ , is in seconds.
a) When does the bungee jumper reach maximum height? Why is it a maximum?
b) What is the maximum height reached by the jumper?
c) Determine the height of the platform from which the bungee jumper jumps.

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Problem 2272

Study the table. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & 8 \\ \hline-1 & 2 \\ \hline 0 & 0 \\ \hline 1 & 2 \\ \hline 2 & 8 \\ \hline \hline \end{tabular}
Which best describes the function represented by the data in the table? linear with a common ratio of 4 linear with a common second difference of 4 quadratic with a common ratio of 4 quadratic with a common second difference of 4

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Problem 2273

Study this table. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-3 & -2 \\ \hline-2 & 0 \\ \hline 0 & 4 \\ \hline 4 & 12 \\ \hline \hline \end{tabular}
Which best describes the function represented by the data in the table? linear with a common ratio of 2 linear with a common first difference of 2 quadratic with a common ratio of 2 quadratic with a common first difference of 2

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Problem 2274

14. For each quadratic relation, i) write the equation in factored form ii) determine the coordinates of the vertex iii) write the equation in vertex form iv) sketch the graph
a) $y = x^2 - 8x + 15$ b) $y = 2x^2 - 8x - 64$ c) $y = -4x^2 - 12x + 7$

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Problem 2275

Solve $(w+1)^{2}-75=0$ , where $w$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with cor If there is no solution, click "No solution." $w=$

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Problem 2276

2. $3(x+1)^{2}-3=0$ . .xis of symmetry: Vertex: Solution(s):

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Problem 2277

Question 1 (Mandatory) (1 point) An amusement park usually charges $\$34$ per ticket, but wants to raise the price by $\$1$ per ticket. The revenue that could be generated is modelled by the function $R(x) = -125(x-12)^2 + 35\,000$ , where $x$ is the number of $\$1$ increases and the revenue, $R(x)$ , is in dollars. What should the ticket price be if the park wants to earn $\$15\,000$ ?

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Problem 2278

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function $P(x) = -22.5x^2 + 428x + 1100$ , where x is the number of years since 1990. According to the model, when will the population be the highest?

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Problem 2279

Question 4 (Mandatory) (1 point) Determine the values of $a$ , $h$ , and $k$ that make the equation. $-3x^2 + 9x - 6 = a(x - h)^2 + k$ .

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Problem 2280

Question 5 (Mandatory) (1 point)
Identify the values of $a$ , $b$ , and $c$ you would use to substitute into the quadratic formula to solve $14x + 20x^2 = 17x - 25$ .

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Problem 2281

Question 6 (Mandatory) (1 point) A rocket is launched into the sky and follows a path modelled by the function $h(t) = -5(t-6.32)^2 + 200$ , where time, $t$ , is in seconds and height, $h(t)$ , is in metres. Approximately how high will the rocket be after 9 seconds?

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Problem 2282

Question 8 (Mandatory) (1 point) Use the quadratic formula to solve $-6x^2 + 5x + 8 = 0$ . Round your answer to two decimal places.

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Problem 2283

Question 9 (Mandatory) (1 point) What is the factored form of $x^2 + 2x + 1$

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Problem 2284

Question 10 (Mandatory) (1 point) Which equation represents $y = -2x^2 - 12x - 7$ in vertex form?

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Problem 2285

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of $f(x) = 4x^2 - 8x + 11$ without graphing the parabola.

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Problem 2286

Question 12 (Mandatory) (1 point)
What number must you add to $x^2 + 12x$ to create a perfect square?

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Problem 2287

Solve for $k$ in the equation: $k^{2}-16=6 k^{3}-96 k$ . What are the real solutions?
$k=$

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Problem 2288

Find the positive value of $k$ so that $9x^{2}+kx+25$ factors as $(ax+b)^{2}$ . Choices: 30, 16, 15, 8, 2.

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Problem 2289

Evaluate $f(x)=-x^{2}-5$ for $f(2)$ and $f(-1)$ . Find $f(2)=\square$ and $f(-1)=\square$ .

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Problem 2290

Given the function $f(x) = 0.4x^2 - 36x + 1000$ for drivers aged 16-74:
1. Calculate and simplify $f(50)$ .
2. Explain $f(50)$ as accidents per 50 million miles for 50-year-olds.
3. Describe $f(50)$ as a point on the graph of $f(x)$ .

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Problem 2291

Find the maximum value of $f(x)=400 x-11 x^{2}-3$ graphically, rounded to four decimal places.

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Problem 2292

Find the intersection of the curves $y=2x^2+3$ and $y=-x+6$ .

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Problem 2293

Find the intersection points of the lines $y=3-x$ and $y=-x^{2}+2x+3$ .

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Problem 2294

Solve the equation $-0.0015 x^{2} + x + 2 = 0$ for $x$ .

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Problem 2295

Solve the equation $-0.0015 x^{2} + x + 2 = 0$ .

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Problem 2296

Simplify the expression $\left[a^{4}-4 a^{2}+4\right]^{\frac{1}{2}}$ .

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Problem 2297

Solve the equation $x^{2}+4x-5=-x+1$ .

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Problem 2298

Does the equation $x = y^{2} + 15$ define $y$ as a function of $x$ ? Choose A, B, C, or D.

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Problem 2299

Solve the equation $2 x^{2}-x-1=2 x+1$ .

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Problem 2300

Solve the equation. $\begin{array}{l} x(x+3)=0 \\ x=\square \end{array}$ (Use a comma to separate answers as nee

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Quadratics

Problem 2201

Find f(−4)f(-4)f(−4) for the function f(x)=x2−2x−6f(x)=x^{2}-2x-6f(x)=x2−2x−6.

Problem 2202

Find ccc if the average value of f(x)=x2+cxf(x)=x^{2}+c xf(x)=x2+cx over [0,7][0,7][0,7] equals 4. Enter your answer as a decimal.

Problem 2203

VideoSolve for s. s2+23s+22=0s^{2}+23 s+22=0s2+23s+22=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. s=s=s= □\square□ Submit

Problem 2204

8x2+112px+8y2−64py=−448p28x^2 + 112px + 8y^2 - 64py = -448p^28x2+112px+8y2−64py=−448p2In the xyxyxy-plane, the graph of the given equation is a circle. The length of the radius of the circle is npnpnp, where nnn and ppp are positive constants. What is the value of nnn?Answer Preview:

Problem 2205

What are the roots of the equation x2−10x+26=0x^{2}-10 x+26=0x2−10x+26=0 in simplest a+bia+b ia+bi form?AnswerAdditional Solution No Solution

Problem 2206

Problem 2207

For the function f(x)=3x2−4f(x)=3 x^{2}-4f(x)=3x2−4, which domain restriction makes f(x)f(x)f(x) invertible? Select from (0,∞)(0, \infty)(0,∞), (−1,∞)(-1, \infty)(−1,∞), or (−4,∞)(-4, \infty)(−4,∞). What is f−1f^{-1}f−1?

Problem 2208

Find the solutions for x2+3.5x−2=0x^2 + 3.5x - 2 = 0x2+3.5x−2=0. Options: A. 0.5 B. -0.5 C. 4 D. -4 E. −7+172\frac{-7+\sqrt{17}}{2}2−7+17​​ F. −7−172\frac{-7-\sqrt{17}}{2}2−7−17​​ G. 7+172\frac{7+\sqrt{17}}{2}27+17​​ H. 7−172\frac{7-\sqrt{17}}{2}27−17​​.

Problem 2209

Select the true equalities for the function g(x)=x2+3x−1g(x)=x^{2}+3x-1g(x)=x2+3x−1: A. g(−4)=3g(-4)=3g(−4)=3, B. g(0)=2g(0)=2g(0)=2, C. g(1)=3g(1)=3g(1)=3, D. g(2)=9g(2)=9g(2)=9, E. g(3)=14g(3)=14g(3)=14.

Problem 2210

Find the domain restriction for f(x)=3x2−4f(x)=3x^{2}-4f(x)=3x2−4 to make it invertible, and identify f−1(x)f^{-1}(x)f−1(x). Options: A, B, C, D.

Problem 2211

Find real solutions using the square root property for: 3n2+240=03 n^{2}+240=03n2+240=0 and 4s2−288=04 s^{2}-288=04s2−288=0. Provide exact answers.

Problem 2212

Solve for xxx using the square root property: 3x2+73=943 x^{2}+73=943x2+73=94. Enter answers as a list, e.g., 4,−234, -\frac{2}{3}4,−32​.

Problem 2213

Solve the equation p2−11p+28=0p^{2}-11p+28=0p2−11p+28=0. Enter your integer or fraction answers separated by commas.

Problem 2214

Solve the equation: z2=19z−84z^{2}=19 z-84z2=19z−84. Find z=z=z=. If multiple solutions, separate with a comma.

Problem 2215

Rewrite x2−8x−4=0x^{2}-8 x-4=0x2−8x−4=0 as (x−p)2=q(x-p)^{2}=q(x−p)2=q.

Problem 2216

Solve the equation z2+14z−49=6z^{2}+14z-49=6z2+14z−49=6 by completing the square. Find the value to add, the equation form, and solutions.

Problem 2217

Solve the equation using the quadratic formula: 3r2−r−1=03 r^{2}-r-1=03r2−r−1=0. List the solutions, separated by commas. r=r=r=

Problem 2218

Find the number and type of solutions for 5x2+5x−2=05x^{2} + 5x - 2 = 05x2+5x−2=0. Options: rational, imaginary, repeated, or irrational.

Problem 2219

If the discriminant of a quadratic equation is 4, what can you say about its solutions?

Problem 2220

If the discriminant of a quadratic equation is -2, what can you say about the equation's roots?

Problem 2221

Problem 2222

Solve 6x2+9x=06x^2 + 9x = 06x2+9x=0x=x =x= (Separate answers by a comma. Write answers as integers or reduced fractions.) Question Help: Video

Problem 2223

4. [Maximum mark: 4] Solve for n: (n2)−2n=20\binom{n}{2} - 2n = 20(2n​)−2n=20

Problem 2224

Find the minimum yyy-value on the graph of y=8x2−32x+37y = 8x^2 - 32x + 37y=8x2−32x+37.The minimum yyy-value is 00\boxed{\phantom{00}}00​.

Problem 2225

y=3x2+90x+50y = 3x^2 + 90x + 50y=3x2+90x+50

Problem 2226

Problem 2227

Problem 2228

QuestionSolve for all values of xxx by factoring. x2+x−16=xx^{2}+x-16=xx2+x−16=xAnswer Attempt 1 out of 3

Problem 2229

Solve the equation 2x2−19x+2=−10x2 x^{2}-19 x+2=-10 x2x2−19x+2=−10x to the nearest tenth.Answer Attempt 1 out of 3 (ค) Additional Solution Θ\ThetaΘ No Solution

Problem 2230

Solve the following inequality algebraically. −3x2+5x>−3x−3-3 x^{2}+5 x>-3 x-3−3x2+5x>−3x−3Answer Attempt 1 out of 3 □\square□

Problem 2231

Problem 2232

Solve by completing the square: z2=12z+1z^{2}=12 z+1z2=12z+1

Problem 2233

x2+y2−6x+8y+16=0x^2 + y^2 - 6x + 8y + 16 = 0x2+y2−6x+8y+16=0

Problem 2234

Problem 2235

Problem 2236

15. (2x−7)(x+5)=0(2 x-7)(x+5)=0(2x−7)(x+5)=0

Problem 2237

The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area ( AAA ) of the room? - A=x(x+5)A=x(x+5)A=x(x+5) A=x+(x+5)A=x+(x+5)A=x+(x+5) A=5xA=5 xA=5x A=2x+2(x+5)A=2 x+2(x+5)A=2x+2(x+5)

Problem 2238

tion list restion 14 vestion 15Find the zerrs of the function aloworracally. f(x)=3x2−x+2f(x)=3 x^{2}-x+2f(x)=3x2−x+2The zeros are □\square□ . (Sinclly your answer: Type an exact answer, using radicals and ias needed. Use inte

Problem 2239

x2+8x+12=0x^2 + 8x + 12 = 0x2+8x+12=0

Problem 2240

Solve the equation x2+8x+17=0x^{2}+8 x+17=0x2+8x+17=0 and express solutions as a+bia+b ia+bi.

Problem 2241

Solve for real values of xxx in the equation (x+9)2−7(x+9)−18=0(x+9)^{2}-7(x+9)-18=0(x+9)2−7(x+9)−18=0.

Problem 2242

Bianca's towel is 16 ft by 28 ft. Use the difference of two squares to find its area. Which expression is correct? 282−16228^{2}-16^{2}282−162

Problem 2243

Given f(x)=5x2−x+2f(x)=5 x^{2}-x+2f(x)=5x2−x+2, find f(−a)f(-a)f(−a), f(a+1)f(a+1)f(a+1), 2f(a)2 f(a)2f(a), f(2a)f(2 a)f(2a), f(a2)f(a^{2})f(a2), [f(a)]2[f(a)]^{2}[f(a)]2, and f(a+h)f(a+h)f(a+h).

Find $f(-4)$ for the function $f(x)=x^{2}-2x-6$ .

Find $c$ if the average value of $f(x)=x^{2}+c x$ over $[0,7]$ equals 4. Enter your answer as a decimal.

Video
Solve for s. $s^{2}+23 s+22=0$
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $s=$ $\square$ Submit

$8x^2 + 112px + 8y^2 - 64py = -448p^2$
In the $xy$ -plane, the graph of the given equation is a circle. The length of the radius of the circle is $np$ , where $n$ and $p$ are positive constants. What is the value of $n$ ?
Answer Preview:

What are the roots of the equation $x^{2}-10 x+26=0$ in simplest $a+b i$ form?
Answer
Additional Solution No Solution

For the function $f(x)=3 x^{2}-4$ , which domain restriction makes $f(x)$ invertible? Select from $(0, \infty)$ , $(-1, \infty)$ , or $(-4, \infty)$ . What is $f^{-1}$ ?

Find the solutions for $x^2 + 3.5x - 2 = 0$ . Options: A. 0.5 B. -0.5 C. 4 D. -4 E. $\frac{-7+\sqrt{17}}{2}$ F. $\frac{-7-\sqrt{17}}{2}$ G. $\frac{7+\sqrt{17}}{2}$ H. $\frac{7-\sqrt{17}}{2}$ .

Select the true equalities for the function $g(x)=x^{2}+3x-1$ : A. $g(-4)=3$ , B. $g(0)=2$ , C. $g(1)=3$ , D. $g(2)=9$ , E. $g(3)=14$ .

Find the domain restriction for $f(x)=3x^{2}-4$ to make it invertible, and identify $f^{-1}(x)$ . Options: A, B, C, D.

Find real solutions using the square root property for: $3 n^{2}+240=0$ and $4 s^{2}-288=0$ . Provide exact answers.

Solve for $x$ using the square root property: $3 x^{2}+73=94$ . Enter answers as a list, e.g., $4, -\frac{2}{3}$ .

Solve the equation $p^{2}-11p+28=0$ . Enter your integer or fraction answers separated by commas.

Solve the equation: $z^{2}=19 z-84$ . Find $z=$ . If multiple solutions, separate with a comma.

Rewrite $x^{2}-8 x-4=0$ as $(x-p)^{2}=q$ .

Solve the equation $z^{2}+14z-49=6$ by completing the square. Find the value to add, the equation form, and solutions.

Solve the equation using the quadratic formula: $3 r^{2}-r-1=0$ . List the solutions, separated by commas. $r=$

Find the number and type of solutions for $5x^{2} + 5x - 2 = 0$ . Options: rational, imaginary, repeated, or irrational.

Solve $6x^2 + 9x = 0$
$x =$ (Separate answers by a comma. Write answers as integers or reduced fractions.) Question Help: Video

4. [Maximum mark: 4] Solve for n: $\binom{n}{2} - 2n = 20$

Find the minimum $y$ -value on the graph of $y = 8x^2 - 32x + 37$ .
The minimum $y$ -value is $\boxed{\phantom{00}}$ .

$y = 3x^2 + 90x + 50$

Question
Solve for all values of $x$ by factoring. $x^{2}+x-16=x$
Answer Attempt 1 out of 3

Solve the equation $2 x^{2}-19 x+2=-10 x$ to the nearest tenth.
Answer Attempt 1 out of 3 (ค) Additional Solution $\Theta$ No Solution

Solve the following inequality algebraically. $-3 x^{2}+5 x>-3 x-3$
Answer Attempt 1 out of 3 $\square$

Solve by completing the square: $z^{2}=12 z+1$

$x^2 + y^2 - 6x + 8y + 16 = 0$

15. $(2 x-7)(x+5)=0$

The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area ( $A$ ) of the room? - $A=x(x+5)$ $A=x+(x+5)$ $A=5 x$ $A=2 x+2(x+5)$

tion list restion 14 vestion 15
Find the zerrs of the function aloworracally. $f(x)=3 x^{2}-x+2$
The zeros are $\square$ . (Sinclly your answer: Type an exact answer, using radicals and ias needed. Use inte

$x^2 + 8x + 12 = 0$

Solve the equation $x^{2}+8 x+17=0$ and express solutions as $a+b i$ .

Solve for real values of $x$ in the equation $(x+9)^{2}-7(x+9)-18=0$ .

Bianca's towel is 16 ft by 28 ft. Use the difference of two squares to find its area. Which expression is correct? $28^{2}-16^{2}$

Given $f(x)=5 x^{2}-x+2$ , find $f(-a)$ , $f(a+1)$ , $2 f(a)$ , $f(2 a)$ , $f(a^{2})$ , $[f(a)]^{2}$ , and $f(a+h)$ .

Factor and solve $4 x^{2}+12 x+5=-4$ . Find the values of $x$ .

Find the max or min of the function: $f(x)=-x^{2}-3x+3$ .

Find the roots of the equation $2x^{2}-13x+20=0$ .

Solve the inequality $f(x) \geq 0$ for $f(x)=(x+4)(x-2)^{2}$ using its graph. Answer in interval notation: $\square$ .

Solve the equation $2x^{2}+7x+6=0$ for the variable $x$ .

Factor and solve the equation $4 a^{2}+11 a-20=0$ . Find values for $a$ :
$a=$ or $a=$

Solve the equation $-6 x^{2}-20 x-16=0$ for $x$ and simplify your answers. If multiple solutions, separate with a comma.

Solve for real $x$ in the equation $x^{2}-10x+23=23$ by completing the square. Find $x_{1}$ and $x_{2}$ with $x_{1}<x_{2}$ .

Factor and solve the equation $4 a^{2}+11 a-20=0$ . Find $a=$ or $a=$ .

Solve the following quadratic equation using the quadratic formula. $-4y^2 - 3y + 4 = 0$

Identify the equation without completing the squares. $8 x^{2}+5 y^{2}-4 x+7 y=0$
Choose the conic that matches the given equation. A. Hyperbola B. Ellipse C. Parabola D. The equation does not represent a conic. E. Circle

22 Solve the following quadratic equations by square roots. Write all answers in simplest form.
$3x^2 - 108 = 0$
$x^2 = 36$
Solution(s):

$9x^2 - 16 = 0$ $x^2 =$ Solution(s):

Solve each quadratic.
1. $3 \cot^2{x} - 3 \cot{x} = 1$

Solve the equation using the quadratic formula. $2 x^{2}-3 x=-5$
The solution set is $\square$ \} (Simplify your answer. Type an exact answer using radicals and $i$ as needed. Use answers as needed.)

11 12 13 14 15 16 17 18
For which value of $m$ does the graph of $y=18 x^{2}+m x+2$ have exactly one $x$ -intercept? 0 9 12 16 Mark this and return Save and Exit Next

Solve $x^{2}-16 x+60=-12$ by completing the steps. First, subtract $\square$ from each side of the equation. DONE

$b = \frac{a+x^2}{3}$ Make x the subject.

Solve the system by the addition method. $\left\{\begin{array}{l} x^{2}-3 y^{2}=-11 \\ 4 x^{2}+y^{2}=8 \end{array}\right.$
The solution set is $\square$ \}. (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

Solve the inequality and graph the solution on the real number line. $(x-4)^{2} \geq 1$

Solve the system by the addition method. $\begin{cases} x^2 - 4y^2 = -32 \\ 2x^2 + y^2 = 17 \end{cases}$ The solution set is $\{\}$ . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

Using the graph, determine the coordinates of the vertex of the parabola.
Answer Attempt 1 out of 2
Answer type Submit Answer
Two points One point One equation

Question
Solve the equation for all real solutions in simplest form. $4 y^{2}-14 y+9=0$