What is the x-intercept of the graph of the function f(x) = x² -16x+64?

Solution:

It is given that

f(x) = x² -16x+64

In order to find the x-intercept we have to take y = 0

x² - 16x + 64 = 0

Splitting the middle term

x² - 8x - 8x + 64 = 0

Taking out the common terms

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

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

So we get

x = 8

To find the y-intercept, we have to take x = 0

f(0) = 0² -16(0)+64

f(0) = 64

Therefore, the x-intercept of the graph of the function f(x) = x² -16x+64 is 8.

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What is the x-intercept of the graph of the function f(x) = x² -16x+64?

Summary:

The x-intercept of the graph of the function f(x) = x² -16x+64 is 8.