Question

Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?

Answer 1

The vertex form is:

`y = - 3{(x + 2)}^(2) +10`

EXPLANATION

The given equation is:

`y = - 3 {x}^(2) - 12x - 2`

`y = - 3( {x}^(2) + 4x) - 2`

We add and subtract the square of half the coefficient of x.

`y = - 3( {x}^(2) + 4x + {2}^(2) ) - - 3( {2})^(2) - 2`

We simplify to get,

`y = - 3{(x + 2)}^(2) + 3(4)- 2`

`y = - 3{(x + 2)}^(2) +10`

This is in the vertex form.

Answer 2

The vertex form is y = -3(x + 2)² + 10

Explanation:

* Lets revise how to put the quadratic in the vertex form

- The general form of the quadratic is y = ax² + bx + c, where

a , b , c are constants

# a is the coefficient of x²

# b is the coefficient of x

# c is the numerical term or the y-intercept

- The vertex form of the quadratic is a(x - h)² + k, where a, h , k

are constants

# a is the coefficient of x²

# h is the x-coordinate of the vertex point of the quadratic

# k is the y-coordinate of the vertex point of the quadratic

- We can find h from a and b ⇒ h = -b/a

- We find k by substitute the value of h instead of x in the general form

of the quadratic

k = ah² + bh + c

* Now lets solve the problem

∵ y = -3x² - 12x - 2

∵ y = ax² + bx + c

∴ a = -3 , b = -12

∵ h = -b/2a

∴ h = -(-12)/2(-3) = 12/-6 = -2

- Lets find k

∴ k = -3(-2)² - 12(-2) - 2 = -3(4) + 24 - 2 = -12 + 24 - 2 = 10

* Lets writ the vertex form

∵ y = a(x - h)² + k

∵ a = -3 , h = -2 , k = 10

∴ y = -3(x - -2)² + 10

∴ y = -3(x + 2)² + 10

* The vertex form is y = -3(x + 2)² + 10