Question

Y = -5 (x + 2)^2 - 10


Convert the equation from vertex form to standard form.

Answer 1

Given:

The vertex form of a quadratic equation is

`y=-5(x+2)^2-10`

To find:

The standard form of the given quadratic equation.

Solution:

We have,

`y=-5(x+2)^2-10`

Using the formula
`(a+b)^2=a^2+2ab+b^2`, we get

`y=-5(x^2+2(x)(2)+(2)^2)-10`

`y=-5(x^2+4x+4)-10`

Using distributive property, we get

`y=-5x^2-20x-20-10`

`y=-5x^2-20x-30`

Therefore, the standard form of the given equation is
`y=-5x^2-20x-30`.