# What is the vertex form of y= 3x^2 - 14x - 24 ?

Aug 17, 2017

Vertex form of given equation is $y = 3 {\left(x - \frac{7}{3}\right)}^{2} - \frac{121}{3}$ and vertex is $\left(\frac{7}{3} , - \frac{121}{3}\right)$

#### Explanation:

Vertex form of such a quadratic equation is $y = a {\left(x - h\right)}^{2} + k$, where vertex is $\left(h , k\right)$.

As $y = 3 {x}^{2} - 14 x - 24$, can be written as

$y = 3 \left({x}^{2} - \frac{14}{3} x\right) - 24$

or $y = 3 \left({x}^{2} - 2 \times \frac{7}{3} \times x + {\left(\frac{7}{3}\right)}^{2} - \frac{49}{9}\right) - 24$

or $y = 3 {\left(x - \frac{7}{3}\right)}^{2} - \frac{49}{3} - 24$

or $y = 3 {\left(x - \frac{7}{3}\right)}^{2} - \frac{121}{3}$ and vertex is $\left(\frac{7}{3} , - \frac{121}{3}\right)$