Question

In the following exercises, find the x- and y-intercepts.

$y=x^2+16x+64$

Short answer

x- intercept is the point$(-8,0)$and y- intercept is the point$(0,64)$.

Step-by-step solution

Given information

The given expression is:$y=x^2+16x+64$

Determine the x- intercept.

Set $y=0$ and solve for x.

$$\begin{gathered} 0=x^2+16x+64 \\ {x}^2+16x+64=0 \end{gathered}$$

Solve the equation using factoring.

$(x+8)(x+8)=0$

$x+8=0$ or $x+8=0$

$x=-8$ or $x=-8$

The result gives that when $y=0$, then $x=-8$

x- intercept is the point $(-8,0)$.

Determine the y- intercept.

Substitute $x=0$and evaluate $y\left(0\right)$.

$$\begin{gathered} y\left(0\right)=0^2+16\left(0\right)+64 \\ =0+0+64 \\ =64 \end{gathered}$$

y- intercept is the point$(0,64)$.