# What is the vertex form of y=4x^2+19x - 5 ?

May 1, 2017

Vertex form of equation is $y = 4 {\left(x + 2.375\right)}^{2} - 27.5625$

#### Explanation:

$y = 4 {x}^{2} + 19 x - 5 \mathmr{and} y = 4 \left({x}^{2} + \frac{19}{4} x\right) - 5 \mathmr{and} y = 4 \left({x}^{2} + \frac{19}{4} x + {19}^{2} / {8}^{2}\right) - 4 \cdot {19}^{2} / {8}^{2} - 5$ or

$y = 4 {\left(x + \frac{19}{8}\right)}^{2} - \frac{361}{16} - 5 \mathmr{and} y = 4 {\left(x + \frac{19}{8}\right)}^{2} - \frac{441}{16}$ or

$y = 4 {\left(x + 2.375\right)}^{2} - 27.5625$ Comparing with standard vertex form of equation y=a(x-h)^2 + k ;(h.k)  being vertex.

We get vertex at $\left(- 2.375 , - 27.5625\right)$

Vertex form of equation is $y = 4 {\left(x + 2.375\right)}^{2} - 27.5625$ [Ans]