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

Dec 25, 2015

There are many ways of finding the vertex form of this type quadratic functions. An easy method is given below.

#### Explanation:

If we have $y = a {x}^{2} + b x + c$ and to write it in vertex form we do the following steps.

If the vertex is $\left(h , k\right)$ then $h = \left(- \frac{b}{2 a}\right)$ and $k = a {\left(h\right)}^{2} + b \left(h\right) + c$

The vertex form is y=a(x-h)^2 + k.

Now let us use the same with our question.

$y = - {x}^{2} - 3 x + 5$

Comparing it with $y = a {x}^{2} + b x + c$ we get $a = - 1$, $b = - 3$, $c = 5$

$h = - \frac{b}{2 a}$
$h = - \frac{- 3}{2 \left(- 1\right)}$
$h = - \frac{3}{2}$

$k = - {\left(- \frac{3}{2}\right)}^{2} - 3 \left(- \frac{3}{2}\right) + 5$
$k = - \frac{9}{4} + \frac{9}{2} + 5$
$k = + \frac{9}{4} + 5$
$k = \frac{9}{4} + \frac{20}{4}$
$k = \frac{29}{4}$

$y = - {\left(x - \left(- \frac{3}{2}\right)\right)}^{2} + \frac{29}{4}$

$y = - {\left(x + \frac{3}{2}\right)}^{2} + \frac{29}{4}$ is the vertex form