# What is the vertex form of y=13x^2 + 14x + 24?

Jul 17, 2018

Vertex form of equation is $y = 13 {\left(x + \frac{7}{13}\right)}^{2} - 20 \frac{3}{13}$

#### Explanation:

$y = 13 {x}^{2} + 14 x + 24$ or

$y = 13 \left({x}^{2} + \frac{14}{13} x\right) + 24$ or

$y = 13 \left\{{x}^{2} + \frac{14}{13} x + {\left(\frac{7}{13}\right)}^{2}\right\} - \frac{49}{13} + 24$ or

$y = 13 {\left(x + \frac{7}{13}\right)}^{2} - \frac{263}{13}$ or

$y = 13 {\left(x + \frac{7}{13}\right)}^{2} - 20 \frac{3}{13}$. Comparing with standard vertex

form of equation  f(x)=a(x-h)^2+k ; (h,k) being vertex

we find here $h = - \frac{7}{13} , k = - 20 \frac{3}{13} \therefore$ Vertex is at

$\left(- \frac{7}{13} , - 20 \frac{3}{13}\right)$ . Vertex form of equation is

$y = 13 {\left(x + \frac{7}{13}\right)}^{2} - 20 \frac{3}{13}$ [Ans]