# What is the vertex form of y= 2x^2 + 5x - 3 ?

Aug 13, 2016

$\text{The form of equation is:}$

$y = 2 {\left(x + \frac{5}{4}\right)}^{2} - \frac{49}{8}$

#### Explanation:

$y = a {x}^{2} + b x + c \text{ Standard form}$

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

$P \left(h , k\right) \text{represents the coordinate of vertex}$

$y = 2 {x}^{2} + 5 x - 3$

a=2" ; "b=5" ; "c=-3)

$h = - \frac{b}{2 a}$

$h = - \frac{5}{2 \cdot 2} = - \frac{5}{4}$

$k = 2 \cdot {\left(- \frac{5}{4}\right)}^{2} + 5 \cdot \left(- \frac{5}{4}\right) - 3$

$k = 2 \cdot \frac{25}{16} - \frac{25}{4} - 3$

$k = \frac{50}{16} - \frac{25}{4} - 3$

$k = \frac{50 - 100 - 48}{16}$

$k = - \frac{49}{8} = - 6.13 \text{ Rounded the two decimal place}$

$\text{The form of equation is:}$

$y = 2 {\left(x + \frac{5}{4}\right)}^{2} - \frac{49}{8}$