Math

QuestionFind the zeros of the function f(x)=x212f(x)=x^{2}-12 using the square root method. What are the xx-intercepts?

Studdy Solution

STEP 1

Assumptions1. The function is a quadratic function given by f(x)=x12f(x)=x^{}-12 . We are to find the zeros of the function using the square root method3. The zeros of a function are the x-values for which the function equals zero4. The x-intercepts of a graph are the points where the graph crosses the x-axis, which are also the zeros of the function

STEP 2

First, we need to set the function equal to zero to find the zeros of the function.
f(x)=x212=0f(x)=x^{2}-12=0

STEP 3

Next, we need to isolate the x2x^{2} term on one side of the equation.
x2=12x^{2}=12

STEP 4

To solve for xx, we take 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=12,12x=\sqrt{12}, -\sqrt{12}

STEP 5

Now, we simplify the square root of12. The square root of12 can be simplified to 232\sqrt{3}.
x=23,23x=2\sqrt{3}, -2\sqrt{3}

STEP 6

The zeros of the function are the solutions we found, which are x=23x=2\sqrt{3} and x=23x=-2\sqrt{3}.

STEP 7

The x-intercepts of the graph are the x-values for which the function equals zero, which are also the zeros of the function. Therefore, the x-intercepts of the graph are also x=23x=2\sqrt{3} and x=23x=-2\sqrt{3}.
So, the correct choice isB. The zeros and the x-intercepts are the same. They are x=23x=2\sqrt{3} and x=23x=-2\sqrt{3}.

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