Question

What is the x-intercept of the graph of the function f(x) = x^2 − 16x + 64? (−8, 0) (0, 8) (8, 0) (0, −8)

Answer 1

Answer:

Choice C is the answer.

Step-by-step explanation:

We have given a function.

f(x) = x² − 16x + 64

We have to find the x-intercept of the graph of function.

x-intercept is a point where the value of function is zero.

Putting f(x) =  in given function , we have

x²-16x+64 = 0

Factoring above equation, we have

x²-8x-8x+64 = 0

x(x-8)-8(x-8) = 0

(x-8)(x-8) = 0

Applying zero-product property , we have

x-8 = 0 or x-8 = 0

Hence, x = 8 when f(x) = 0

x-intercept is (8,0).

Answer 2

Answer:

(8, 0)

Step-by-step explanation:

The x-intercepts are the roots or solutions of a quadratic equation. To solve this equation use the quadratic formula.

$\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

In this equation, a = 1, b = -16, and c = 64. Substitute these values into the formula.

$\frac{-(-16)\pm\sqrt{(-16)^2-4(1)(64)}}{2(1)}\rightarrow \frac{16\pm\sqrt{256-4(64)} }{2} \rightarrow \frac{16\pm\sqrt{0} }{2}$

After simplifying, you are left with 16/2 which is 8.

The x-intercept of the graph of this function is (8, 0).