# How do you graph and label the vertex and axis of symmetry of y=3(x-1)(x-4)?

Jul 17, 2017

Vertex $\left(2.5 , - 6.75\right)$

Axis of Symmetry $x = 2.5$

#### Explanation:

Given -

$y = 3 \left(x - 1\right) \left(x - 4\right)$

Let us rewrite it as -

$y = \left(3 x - 3\right) \left(x - 4\right)$
$y = 3 {x}^{2} - 3 x - 12 x + 12$
$y = 3 {x}^{2} - 15 x + 12$

Vertex -

$x = \frac{- b}{2 a} = \frac{- \left(- 15\right)}{2 \times 3} = \frac{15}{6} = \frac{5}{2}$

At $x = \frac{5}{2} = 2.5$

$y = 3 {\left(2.5\right)}^{2} - 15 \left(2.5\right) + 12$
$y = 18.75 - 37.5 + 12 = - 6.75$

Vertex $\left(2.5 , - 6.75\right)$

Axis of Symmetry $x = 2.5$

Take a few values on either side of $x = 2.5$
Find the corresponding y value. Tabulate them and plot them.