How do you write f(x)= 2x^2+6x  into vertex form?

May 4, 2017

$y = 2 {\left(x + 1.5\right)}^{2} - 4.5$

Explanation:

Given -

$y = 2 {x}^{2} + 6 x$

First, find the vertex

Find $x$ coordinate of the vertex

$x = \frac{- b}{2 a} = \frac{- 6}{2 \times 2} = - \frac{6}{4} = - 1.5$
Find $y$ coordinat of the vertex
$y = 2 {\left(- 1.5\right)}^{2} + 6 \left(- 1.5\right)$
$y = 2 \left(2.25\right) - 9$

$y = 4.5 - 9 = - 4.5$

Vertex $\left(- 1.5 , - 4.5\right)$

The vertex form of the parabola is -

$y = a {\left(x - h\right)}^{2} - k$

Where -

$a = 2$ the coefficient of ${x}^{2}$
$h = - 1.5$ this is $x$coordinate of the vertex
$k = - 4.5$ this is $y$ coordinate of the vertex

Substitute these values.

$y = 2 {\left(x - \left(- 1.5\right)\right)}^{2} + \left(- 4.5\right)$
$y = 2 {\left(x + 1.5\right)}^{2} - 4.5$
enter link description here