Answer:
The vertex form is y = -3(x + 2)² + 10
Step-by-step 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
