How do I use the vertex formula to determine the vertex of the graph for 2x^2+4x-5?

May 1, 2015

We need to convert $y = 2 {x}^{2} + 4 x - 5$ into its vertex form:
$y = m {\left(x - a\right)}^{2} + b$
(which will then provide the vertex as $\left(a , b\right)$)

$y = 2 {x}^{2} + 4 x - 5$

$y = 2 \left({x}^{2} + 2 x\right) - 5$

$y = 2 \left({x}^{2} + 2 x + 1\right) - 5 - 2$

$y = 2 \left(x + 1\right) - 7$

$y = 2 \left(x - \left(- 1\right)\right) + \left(- 7\right)$

The vertex is at $\left(- 1 , - 7\right)$

May 1, 2015

There is another way.
Coordinates of vertex:
$x = - \frac{b}{2 a}$
$y = f \left[- \frac{b}{2 a}\right]$.

In this example:

$x = - \frac{b}{2 a} = - \frac{4}{4} = - 1$

$f \left(- 1\right) = 2 {\left(- 1\right)}^{2} + 4 \left(- 1\right) - 5 = 2 - 4 - 5 = - 7$