# How do you find the vertex and intercepts for y = x^2 - 4x - 2?

May 1, 2017

y intercept: $\textcolor{red}{- 2}$
vertex at color(red)(""(x,y)=(2,-6))

#### Explanation:

The y-intercept is the value of $y$ when $x = 0$ (that is for point on the Y-axis)
for the given equation
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 4 x - 2$
replacing $x$ with $0$ gives
$\textcolor{w h i t e}{\text{XXX}} y = {0}^{2} - 4 \ast 0 - 2 = - 2$

The easiest way to find the vertex is to convert the given equation into "vertex form": $y = m {\left(x - a\right)}^{2} + b$ with vertex at $\left(a , b\right)$
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 4 x - 2$

$\textcolor{w h i t e}{\text{XXX}} y = 1 \left({x}^{2} - 4 x \textcolor{m a \ge n t a}{+ 4}\right) - 2 \textcolor{m a \ge n t a}{- 4}$

$\textcolor{w h i t e}{\text{XXX}} y = 1 {\left(x - 2\right)}^{2} - 6$
which is the vertex form with vertex at $\left(2 , - 6\right)$

For verification purposes, here is teh graph of the original equation:
graph{x^2-4x-2 [-4.636, 7.854, -6.12, 0.12]}