Use factoring to find the zeros of the quadratic function. List the x-intercepts of the graph of the function.
-$$f ( x ) = x ^ { 2 } - 64$$
A) x = -8
B) x = 8
C) x = -8, x = 8
D) x = -4096, x = 4096

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = x^2 - 64$ can be factored using the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$, where $a = x$ and $b = 8$. Thus, $f(x) = (x - 8)(x + 8)$. Setting $f(x) = 0$ gives the equations $x - 8 = 0$ and $x + 8 = 0$, which have solutions $x = 8$ and $x = -8$, respectively. Therefore, the zeros of the function are $x = -8$ and $x = 8$, corresponding to the x-intercepts of the graph.

Use Factoring to Find the Zeros of the Quadratic Function f(x)=x2−64f ( x ) = x ^ { 2 } - 64f(x)=x2−64

Use Factoring to Find the Zeros of the Quadratic Function $f ( x ) = x ^ { 2 } - 64$