QuestionFind the zeros of $f(x)=x^{2}-24$ using the square root method. What are the $x$ -intercepts?

Studdy Solution

STEP 1

Assumptions1. The function given is a quadratic function, $f(x)=x^{}-24$ . We are asked to find the zeros of the function using the square root method3. We are also asked to find the $x$ -intercepts of the graph of the function4. The zeros of a function are the $x$ values for which the function equals zero5. The $x$ -intercepts of a graph are the points where the graph intersects the $x$ -axis, which are also the zeros of the function

STEP 2

To find the zeros of the function, we need to set the function equal to zero and solve for $x$ . $f(x) =0$ $x^{2}-24 =0$

STEP 3

Now, we need to isolate $x^{2}$ on one side of the equation. We can do this by adding24 to both sides of the equation.
$x^{2} =24$

STEP 4

To solve for $x$ , we need to take the square root of both sides of the equation. Remember, when we take the square root of both sides, we must consider both the positive and negative square roots.
$x = \pm \sqrt{24}$

STEP 5

implify the square root of24. The square root of24 can be simplified to $2\sqrt{}$ , because $24 =4 \times$ and the square root of4 is2.
$x = \pm2\sqrt{}$

STEP 6

The zeros of the function are the $x$ values we just found. So, the zeros of the function are $x =2\sqrt{6}$ and $x = -2\sqrt{6}$ .

STEP 7

The $x$ -intercepts of the graph of the function are the points where the graph intersects the $x$ -axis. These points are also the zeros of the function. Therefore, the $x$ -intercepts are $x =2\sqrt{6}$ and $x = -2\sqrt{6}$ .
The zeros and the $x$ -intercepts are the same. They are $x =2\sqrt{6}$ and $x = -2\sqrt{6}$ .

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QuestionFind the zeros of $f(x)=x^{2}-24$ 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 $x$ . $f(x) =0$ $x^{2}-24 =0$

STEP 3

Now, we need to isolate $x^{2}$ on one side of the equation. We can do this by adding24 to both sides of the equation.
$x^{2} =24$

STEP 4

To solve for $x$ , we need to take the square root of both sides of the equation. Remember, when we take the square root of both sides, we must consider both the positive and negative square roots.
$x = \pm \sqrt{24}$

STEP 5

implify the square root of24. The square root of24 can be simplified to $2\sqrt{}$ , because $24 =4 \times$ and the square root of4 is2.
$x = \pm2\sqrt{}$

STEP 6

The zeros of the function are the $x$ values we just found. So, the zeros of the function are $x =2\sqrt{6}$ and $x = -2\sqrt{6}$ .

STEP 7

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QuestionFind the zeros of f(x)=x2−24f(x)=x^{2}-24f(x)=x2−24 using the square root method. What are the xxx-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)=0x2−24=0x^{2}-24 =0x2−24=0

STEP 3

Now, we need to isolate x2x^{2}x2 on one side of the equation. We can do this by adding24 to both sides of the equation.x2=24x^{2} =24x2=24

STEP 4

To solve for xxx, we need to take the square root of both sides of the equation. Remember, when we take the square root of both sides, we must consider both the positive and negative square roots.x=±24x = \pm \sqrt{24}x=±24​

STEP 5

implify the square root of24. The square root of24 can be simplified to 22\sqrt{}2​, because 24=4×24 =4 \times24=4× and the square root of4 is2.x=±2x = \pm2\sqrt{}x=±2​

STEP 6

The zeros of the function are the xxx values we just found. So, the zeros of the function are x=26x =2\sqrt{6}x=26​ and x=−26x = -2\sqrt{6}x=−26​.

STEP 7

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QuestionFind the zeros of $f(x)=x^{2}-24$ 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 $x$ . $f(x) =0$ $x^{2}-24 =0$

Now, we need to isolate $x^{2}$ on one side of the equation. We can do this by adding24 to both sides of the equation.
$x^{2} =24$

To solve for $x$ , we need to take the square root of both sides of the equation. Remember, when we take the square root of both sides, we must consider both the positive and negative square roots.
$x = \pm \sqrt{24}$

implify the square root of24. The square root of24 can be simplified to $2\sqrt{}$ , because $24 =4 \times$ and the square root of4 is2.
$x = \pm2\sqrt{}$

The zeros of the function are the $x$ values we just found. So, the zeros of the function are $x =2\sqrt{6}$ and $x = -2\sqrt{6}$ .