# What is the vertex form of y=2x^2+9x-5 ?

Jun 25, 2018

Vertex form of equation is $y = 2 {\left(x + 2.25\right)}^{2} - 15.125$

#### Explanation:

$y = 2 {x}^{2} + 9 x - 5$ or

$y = 2 \left({x}^{2} + 4.5 x\right) - 5$ or

$y = 2 \left({x}^{2} + 4.5 x + {2.25}^{2}\right) - 2 \cdot {2.25}^{2} - 5$ or

$2 \cdot {2.25}^{2}$ is added and subtracted to get square.

$y = 2 {\left(x + 2.25\right)}^{2} - 15.125$

Vertex is at $- 2.25 , - 15.125$

Vertex form of equation is $y = 2 {\left(x + 2.25\right)}^{2} - 15.125$ [Ans]