Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

The intercepts of the equation $y=x^2-9$ are

Step-by-Step Solution

Answer

x intercepts are -3  and 3

y intercept is -9

Step 1 : Given information

Given equation is

$y=x^2-9$

Step 2: x intercepts

To find the x-intercept(s)  of an equation, let y = 0 in the equation and solve for x, 

$$\begin{gathered} y=x^2-9 \\ 0=x^2-9 \\ 9=x^2 \\ {x}^2=9 \\ x=\sqrt{9} \\ x=\pm 3 \\ x=3, x=-3 \end{gathered}$$

x intercepts are -3, 3

Step 3: y intercept

To find the y-intercept(s)  of an equation, let x = 0 in the equation and solve for y

$$\begin{gathered} y=x^2-9 \\ y={\left(0\right)}^2-9 \\ y=-9 \end{gathered}$$

y intercept is -9