# What are the x– and y–intercepts of the quadratic equation y = (x – 3)^2 – 25?

Feb 5, 2016

y-intercept: $\left(- 16\right)$
x-intercepts: $8$ and $\left(- 2\right)$

#### Explanation:

The y-intercept is the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x - 3\right)}^{2} - 25$ with $x = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = {\left(0 - 3\right)}^{2} - 25 = 9 - 25 = - 16$

The x-intercept(s) is/are the value(s) of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x - 3\right)}^{2} - 25$ with $y = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 0 = {\left(x - 3\right)}^{2} - 25$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 25 = {\left(x - 3\right)}^{2}$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow {\left(x - 3\right)}^{2} = 25$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x - 3 = \pm 5$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 8 \mathmr{and} x = - 2$