Question

find the intercepts and graph the equation by plotting points.
y = x² - 9
what are the intercepts? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the intercept(s) is/are.
(use a comma to separate answers as needed. type an ordered pair.)
b. there are no intercepts.
use the graphing tool to graph the equation.
click to enlarge graph

Explanation:

Step1: Find x-intercepts (set y=0)

Set $y=0$, solve $0=x^2-9$
$x^2=9$
$x=\pm3$
So x-intercepts are $(-3,0)$ and $(3,0)$.

Step2: Find y-intercept (set x=0)

Set $x=0$, solve $y=0^2-9$
$y=-9$
So y-intercept is $(0,-9)$.

Answer:

A. The intercept(s) is/are $(-3, 0), (3, 0), (0, -9)$

To graph the equation:

1. Plot the intercepts $(-3, 0)$, $(3, 0)$, and $(0, -9)$.
2. Plot additional points (e.g., $x=1$, $y=1^2-9=-8$ so $(1,-8)$; $x=-1$, $y=(-1)^2-9=-8$ so $(-1,-8)$; $x=2$, $y=2^2-9=-5$ so $(2,-5)$; $x=-2$, $y=(-2)^2-9=-5$ so $(-2,-5)$).
3. Draw a smooth, upward-opening parabola connecting all the points, centered on the y-axis (since the equation is a quadratic with no $x$ term, vertex at $(0,-9)$).