# What is the axis of symmetry and vertex for the graph y=4x^2-12x+9?

Feb 28, 2016

color(blue)("Axis of symmetry is "x=3/2
$\textcolor{b l u e}{{x}_{\text{vertex}} = + \frac{3}{2}}$

$\textcolor{b r o w n}{\text{Substitution of "x_("vertex ")" will give you "y_("vertex}}$

#### Explanation:

A really cool trick"

Write as:$\text{ } y = 4 \left({x}^{2} - \frac{12}{4} x\right) + 9$

From the $- \frac{12}{4} x$ apply the process$\text{ } \left(- \frac{1}{2}\right) \times \left(- \frac{12}{4}\right) = + \frac{6}{4} = \frac{3}{2}$

$\textcolor{b l u e}{{x}_{\text{vertex}} = + \frac{3}{2}}$

By substitution you will derive ${y}_{\text{vertex}}$

color(blue)("Axis of symmetry is "x=3/2