Question

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

Answer 1

The vertex is `(-3/5,9)`.

Explanation:

`y=-25x^2-30x` is a quadratic equation in standard form, `ax^2+bx+c`, where `a=-25, b=-30, 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=(-b)/(2a)`. Then substitute the value for `x` into the original equation and solve for `y`.

`x=-(-30)/((2)(-25))`

Simplify.

`x=(30)/(-50)`

Simplify.

`x=-3/5`

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

`y=-25x^2-30x`

`y=-25(-3/5)^2-30(-3/5)`

Simplify.

`y=-25(9/25)+90/5`

Simplify.

`y=-cancel25(9/cancel25)+90/5`

`y=-9+90/5`

Simplify `90/5` to `18`.

`y=-9+18`

`y=9`

The vertex is `(-3/5,9)`.

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