# What is the vertex of  y= 3x^2+8x-7?

Apr 29, 2017

Vertex is at $\left(- 1 \frac{1}{3} , - 12 \frac{1}{3}\right)$

#### Explanation:

$y = 3 {x}^{2} + 8 x - 7$ . Comparing with standard equation $y = a {x}^{2} + b x + c$ we get here $a = 3 , b = 8 , c = - 7$

x co-ordinate of vertex is $- \frac{b}{2 a} \mathmr{and} - \frac{8}{2 \cdot 3} = - \frac{4}{3} = - 1 \frac{1}{3}$ .

Putting the value of $x = - \frac{4}{3}$ we get y co-ordinate of vertex as

$y = 3 \cdot {\left(- \frac{4}{3}\right)}^{2} + 8 \cdot \left(- \frac{4}{3}\right) - 7 = \frac{16}{3} - \frac{32}{3} - 7 = - \frac{16}{3} - 7 = - \frac{37}{3} = - 12 \frac{1}{3}$

Vertex is at $\left(- 1 \frac{1}{3} , - 12 \frac{1}{3}\right)$ [Ans]