Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

List the intercepts of the equation $y=x^2-9$.

Step-by-Step Solution

Answer

The x-intercepts are $(-3,0),(3,0)$, and the y-intercept is $(0,-9)$.

Step 1. Given information.

The given equation is:

$y=x^2-9$

Step 2. Determine the intercepts.

Substitute $y=0$ in the given equation to find the x-intercepts.

$\begin{array}{rcl}0& =& x^2-9\\ 9& =& x^2\\ \pm \sqrt{9}& =& x\\ \pm 3& =& x\end{array}$

Substitute $x=0$ in the given equation to find the y-intercept.

$\begin{array}{rcl}y& =& {\left(0\right)}^2-9\\ y& =& -9\end{array}$

Step 3. Conclusion.

The x-intercepts are $(-3,0), (3,0)$ and the y-intercept is $(0,-9)$.