Math / Algebra

Question27) Solve the quadratic by Graphing on Desmos: $-2 x^{2}+12 x=17$ \begin{tabular}{|l|l|} \hline A. $x=2.50$ and 3.59 & C. $x=2.293$ and 3.707 \\ \hline B. $x=-1.183$ and 7.183 & D. No Real Solutions \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? Find the values of $x$ that make this equation true: $-2x^2 + 12x = 17$ , and we're encouraged to use a graphing tool. Watch out! Make sure to rearrange the equation correctly before graphing!
Also, remember to check if the solutions from the graph actually satisfy the original equation.

STEP 2

1. Rewrite the equation
2. Graph the equation
3. Find the solutions

STEP 3

We want to solve $-2x^2 + 12x = 17$ .
To solve by graphing, we need one side of the equation to be zero.
Let's subtract $17$ from both sides of the equation:
$-2x^2 + 12x - 17 = 17 - 17$ $-2x^2 + 12x - 17 = 0$

STEP 4

Now, our equation looks like $f(x) = 0$ , which is perfect for graphing!

STEP 5

Now, let's graph the equation $y = -2x^2 + 12x - 17$ using a graphing tool like Desmos.
We're looking for the points where the graph crosses the $x$ -axis, also known as the $x$ -intercepts.
These are the points where $y = 0$ , which is exactly what we want!

STEP 6

When we graph it, we see the parabola intersects the x-axis at approximately $x = 2.293$ and $x = 3.707$ .

STEP 7

The $x$ -intercepts we found from the graph are our solutions!
They are the values of $x$ that make our equation $-2x^2 + 12x - 17 = 0$ true.

STEP 8

So, our solutions are approximately $x = \mathbf{2.293}$ and $x = \mathbf{3.707}$ .

STEP 9

The solutions to the equation $-2x^2 + 12x = 17$ are approximately $x = 2.293$ and $x = 3.707$ , which corresponds to answer choice C.

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Question27) Solve the quadratic by Graphing on Desmos: $-2 x^{2}+12 x=17$ \begin{tabular}{|l|l|} \hline A. $x=2.50$ and 3.59 & C. $x=2.293$ and 3.707 \\ \hline B. $x=-1.183$ and 7.183 & D. No Real Solutions \\ \hline \end{tabular}

Studdy Solution

STEP 1

STEP 2

1. Rewrite the equation
2. Graph the equation
3. Find the solutions

STEP 3

We want to solve $-2x^2 + 12x = 17$ .
To solve by graphing, we need one side of the equation to be zero.
Let's subtract $17$ from both sides of the equation:
$-2x^2 + 12x - 17 = 17 - 17$ $-2x^2 + 12x - 17 = 0$

STEP 4

Now, our equation looks like $f(x) = 0$ , which is perfect for graphing!

STEP 5

Now, let's graph the equation $y = -2x^2 + 12x - 17$ using a graphing tool like Desmos.
We're looking for the points where the graph crosses the $x$ -axis, also known as the $x$ -intercepts.
These are the points where $y = 0$ , which is exactly what we want!

STEP 6

When we graph it, we see the parabola intersects the x-axis at approximately $x = 2.293$ and $x = 3.707$ .

STEP 7

The $x$ -intercepts we found from the graph are our solutions!
They are the values of $x$ that make our equation $-2x^2 + 12x - 17 = 0$ true.

STEP 8

So, our solutions are approximately $x = \mathbf{2.293}$ and $x = \mathbf{3.707}$ .

STEP 9

The solutions to the equation $-2x^2 + 12x = 17$ are approximately $x = 2.293$ and $x = 3.707$ , which corresponds to answer choice C.

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Question27) Solve the quadratic by Graphing on Desmos: −2x2+12x=17-2 x^{2}+12 x=17−2x2+12x=17 \begin{tabular}{|l|l|} \hline A. x=2.50x=2.50x=2.50 and 3.59 & C. x=2.293x=2.293x=2.293 and 3.707 \\ \hline B. x=−1.183x=-1.183x=−1.183 and 7.183 & D. No Real Solutions \\ \hline \end{tabular}

Studdy Solution

STEP 1

STEP 2

1. Rewrite the equation2. Graph the equation3. Find the solutions

STEP 3

STEP 4

Now, our equation looks like f(x)=0f(x) = 0f(x)=0, which is perfect for graphing!

STEP 5

Now, let's graph the equation y=−2x2+12x−17y = -2x^2 + 12x - 17y=−2x2+12x−17 using a graphing tool like Desmos.We're looking for the points where the graph crosses the xxx-axis, also known as the xxx-**intercepts**.These are the points where y=0y = 0y=0, which is exactly what we want!

STEP 6

When we graph it, we see the parabola intersects the x-axis at approximately x=2.293x = 2.293x=2.293 and x=3.707x = 3.707x=3.707.

STEP 7

The xxx-**intercepts** we found from the graph are our solutions!They are the values of xxx that make our equation −2x2+12x−17=0-2x^2 + 12x - 17 = 0−2x2+12x−17=0 true.

STEP 8

So, our solutions are approximately x=2.293x = \mathbf{2.293}x=2.293 and x=3.707x = \mathbf{3.707}x=3.707.

STEP 9

The solutions to the equation −2x2+12x=17-2x^2 + 12x = 17−2x2+12x=17 are approximately x=2.293x = 2.293x=2.293 and x=3.707x = 3.707x=3.707, which corresponds to answer choice C.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question27) Solve the quadratic by Graphing on Desmos: $-2 x^{2}+12 x=17$ \begin{tabular}{|l|l|} \hline A. $x=2.50$ and 3.59 & C. $x=2.293$ and 3.707 \\ \hline B. $x=-1.183$ and 7.183 & D. No Real Solutions \\ \hline \end{tabular}

1. Rewrite the equation
2. Graph the equation
3. Find the solutions

Now, our equation looks like $f(x) = 0$ , which is perfect for graphing!

Now, let's graph the equation $y = -2x^2 + 12x - 17$ using a graphing tool like Desmos.
We're looking for the points where the graph crosses the $x$ -axis, also known as the $x$ -intercepts.
These are the points where $y = 0$ , which is exactly what we want!

When we graph it, we see the parabola intersects the x-axis at approximately $x = 2.293$ and $x = 3.707$ .

The $x$ -intercepts we found from the graph are our solutions!
They are the values of $x$ that make our equation $-2x^2 + 12x - 17 = 0$ true.

So, our solutions are approximately $x = \mathbf{2.293}$ and $x = \mathbf{3.707}$ .

The solutions to the equation $-2x^2 + 12x = 17$ are approximately $x = 2.293$ and $x = 3.707$ , which corresponds to answer choice C.