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 $y=-5x^2-20x-30$.