# What is the vertex form of y= -25x^2 − 30x ?

Jan 12, 2016

The vertex is $\left(- \frac{3}{5} , 9\right)$.

#### Explanation:

$y = - 25 {x}^{2} - 30 x$ is a quadratic equation in standard form, $a {x}^{2} + b x + c$, where $a = - 25 , b = - 30 , \mathmr{and} c = 0$. The graph of a quadratic equation is a parabola.

The vertex of a parabola is its minimum or maximum point. In this case it will be the maximum point because a parabola in which $a < 0$ opens downward.

Finding the Vertex
First determine the axis of symmetry, which will give you the $x$ value. The formula for the axis of symmetry is $x = \frac{- b}{2 a}$. Then substitute the value for $x$ into the original equation and solve for $y$.

$x = - \frac{- 30}{\left(2\right) \left(- 25\right)}$

Simplify.

$x = \frac{30}{- 50}$

Simplify.

$x = - \frac{3}{5}$

Solve for y.
Substitute the value for $x$ into the original equation and solve for $y$.

$y = - 25 {x}^{2} - 30 x$

$y = - 25 {\left(- \frac{3}{5}\right)}^{2} - 30 \left(- \frac{3}{5}\right)$

Simplify.

$y = - 25 \left(\frac{9}{25}\right) + \frac{90}{5}$

Simplify.

$y = - \cancel{25} \left(\frac{9}{\cancel{25}}\right) + \frac{90}{5}$

$y = - 9 + \frac{90}{5}$

Simplify $\frac{90}{5}$ to $18$.

$y = - 9 + 18$

$y = 9$

The vertex is $\left(- \frac{3}{5} , 9\right)$.

graph{y=-25x^2-30x [-10.56, 9.44, 0.31, 10.31]}