# What is the the vertex of y = 7x^2 - 2x-12 ?

Jun 2, 2017

Vertex of $y = 7 {x}^{2} - 2 x - 12$ is $\left(\frac{1}{7} , - \frac{85}{7}\right)$

#### Explanation:

$y = 7 {x}^{2} - 2 x - 12$

$= 7 \left({x}^{2} - \frac{2}{7} x\right) - 12$

$= 7 \left({x}^{2} - 2 \times \frac{1}{7} \times x + {\left(\frac{1}{7}\right)}^{2}\right) - \frac{1}{7} - 12$

$= 7 {\left(x - \frac{1}{7}\right)}^{2} - \frac{85}{7}$

Now the equation is in vertex form $y = a {\left(x - h\right)}^{2} + k$, whose vertex is $\left(h , k\right)$

Hence vertex of $7 {x}^{2} - 2 x - 12$ is $\left(\frac{1}{7} , - \frac{85}{7}\right)$

graph{7x^2-2x-12 [-3, 3, -15.92, 4.08]}