# What is the vertex form of y=-5x^2-3x+1?

Apr 29, 2017

$y = - 5 {\left(x + \frac{3}{10}\right)}^{2} + \frac{29}{20}$

#### Explanation:

We need to transform this function into this type $y = a {\left(x - h\right)}^{2} + k$
So$y = - 5 {x}^{2} - 3 x + 1$
$\implies y = - 5 \left({x}^{2} + \frac{3}{5} x\right) + 1$
$\implies y = - 5 \left({x}^{2} + \frac{3}{5} x + \frac{9}{100}\right) + 1 + \frac{9}{20}$
Final
$\implies y = - 5 {\left(x + \frac{3}{10}\right)}^{2} + \frac{29}{20}$