QuestionFind the zeros of $f(x) = x^2 - 150$ using the square root method. What are the x-intercepts?

Studdy Solution

STEP 1

Assumptions1. The function is a quadratic function given by $f(x)=x^{}-150$ . We are to find the zeros of the function using the square root method3. The zeros of a function are the x-values where the function equals zero4. The x-intercepts of a function are the x-values where the function crosses or touches the x-axis, which is also where the function equals zero

STEP 2

To find the zeros of the function, we need to set the function equal to zero and solve for $x$ .
$f(x) =0$ $x^{2}-150 =0$

STEP 3

We can solve for $x$ by adding150 to both sides of the equation.
$x^{2} =150$

STEP 4

Now, we can find the values of $x$ by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x = \pm \sqrt{150}$

STEP 5

implify the square root.
$x = \pm \sqrt{25 \times}$

STEP 6

Further simplify the square root by taking the square root of25.
$x = \pm5\sqrt{6}$ The zeros of the function are $x =5\sqrt{6}$ and $x = -5\sqrt{6}$ .

STEP 7

The x-intercepts of a function are the x-values where the function equals zero. Since the zeros of the function are the x-values where the function equals zero, the zeros and the x-intercepts of the function are the same.
The zeros and the $x$ -intercepts are the same. They are $x =5\sqrt{6}$ and $x = -5\sqrt{6}$ .

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QuestionFind the zeros of $f(x) = x^2 - 150$ using the square root method. What are the x-intercepts?

Studdy Solution

STEP 1

STEP 2

To find the zeros of the function, we need to set the function equal to zero and solve for $x$ .
$f(x) =0$ $x^{2}-150 =0$

STEP 3

We can solve for $x$ by adding150 to both sides of the equation.
$x^{2} =150$

STEP 4

Now, we can find the values of $x$ by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x = \pm \sqrt{150}$

STEP 5

implify the square root.
$x = \pm \sqrt{25 \times}$

STEP 6

Further simplify the square root by taking the square root of25.
$x = \pm5\sqrt{6}$ The zeros of the function are $x =5\sqrt{6}$ and $x = -5\sqrt{6}$ .

STEP 7

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QuestionFind the zeros of f(x)=x2−150f(x) = x^2 - 150f(x)=x2−150 using the square root method. What are the x-intercepts?

Studdy Solution

STEP 1

STEP 2

To find the zeros of the function, we need to set the function equal to zero and solve for xxx.f(x)=0f(x) =0f(x)=0x2−150=0x^{2}-150 =0x2−150=0

STEP 3

We can solve for xxx by adding150 to both sides of the equation.x2=150x^{2} =150x2=150

STEP 4

Now, we can find the values of xxx by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.x=±150x = \pm \sqrt{150}x=±150​

STEP 5

implify the square root.x=±25×x = \pm \sqrt{25 \times}x=±25×​

STEP 6

Further simplify the square root by taking the square root of25.x=±56x = \pm5\sqrt{6}x=±56​The zeros of the function are x=56x =5\sqrt{6}x=56​ and x=−56x = -5\sqrt{6}x=−56​.

STEP 7

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QuestionFind the zeros of $f(x) = x^2 - 150$ using the square root method. What are the x-intercepts?

To find the zeros of the function, we need to set the function equal to zero and solve for $x$ .
$f(x) =0$ $x^{2}-150 =0$

We can solve for $x$ by adding150 to both sides of the equation.
$x^{2} =150$

Now, we can find the values of $x$ by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x = \pm \sqrt{150}$

implify the square root.
$x = \pm \sqrt{25 \times}$

Further simplify the square root by taking the square root of25.
$x = \pm5\sqrt{6}$ The zeros of the function are $x =5\sqrt{6}$ and $x = -5\sqrt{6}$ .