Question

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

$y=x^2-8x+15$

Short answer

xintercept is the point$(3,0)$and$(5,0)$,y intercept is the pointlocalid="1657798182348" $(0,15)$

Step-by-step solution

Given information

The given equation is: $y=x^2-8x+15$

Determine the x intercepts.

For xintercept, set $y=0$ and solve for x.

$$\begin{gathered} 0=x^2-8x+15 \\ {x}^2-8x+15=0 \end{gathered}$$

Solve the using factoring.

localid="1653586242685" $$\begin{gathered} (x-3)(x-5)=0 \\ x-3=0orx-5=0 \\ x=3orx=5 \end{gathered}$$

The result gives that when $y=0$, then$x=3$and $x=5$.

x-intercept is the point $(3,0)$and $(5,0)$.

Determine the y intercepts.

Substitute $x=0$and evaluate

localid="1657798250276" $$\begin{gathered} y={\left(0\right)}^2-8\left(0\right)+15 \\ =0+0+15 \\ =15 \end{gathered}$$

y-intercept is the point localid="1657798255842" $(0,15)$.