Find the x and y Intercepts f(x)=x^2-16x+64

$f (x) = x^{2} - 16 x + 64$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x^{2} - 16 x + 64$

Solve the equation.

Rewrite the equation as $x^{2} - 16 x + 64 = 0$ .

$x^{2} - 16 x + 64 = 0$

Factor using the perfect square rule.

Rewrite $64$ as $8^{2}$ .

$x^{2} - 16 x + 8^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$16 x = 2 \cdot x \cdot 8$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 8 + 8^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 8$ .

${(x - 8)}^{2} = 0$

Set the $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

x-intercept(s) in point form.

x-intercept(s): $(8, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = {(0)}^{2} - 16 \cdot 0 + 64$

Solve the equation.

Remove parentheses.

$y = 0^{2} - 16 \cdot 0 + 64$

Remove parentheses.

$y = {(0)}^{2} - 16 \cdot 0 + 64$

Simplify ${(0)}^{2} - 16 \cdot 0 + 64$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = 0 - 16 \cdot 0 + 64$

Multiply $- 16$ by $0$ .

$y = 0 + 0 + 64$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 64$

Add $0$ and $64$ .

$y = 64$

y-intercept(s) in point form.

y-intercept(s): $(0, 64)$

Step 3

List the intersections.

x-intercept(s): $(8, 0)$

y-intercept(s): $(0, 64)$

Step 4

Find the x and y Intercepts f(x)=x^2-16x+64

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