College Algebra word problems

Question

Find the maximum value of the quadratic function.

y = −3x^ ² − 6x − 24

Answer 1

Hello, thank you for taking the time to post your question!

Since the coefficient on the opening term here is negative, that means that the parabola opens downward and the max value occurs at the vertex

x = -b/2a = -(-6) / 2(-3) = 6/-6 = -1

then to find the max function value you can plug x = -1 back into the original function

y = -3(-1)^2 – 6(-1) – 24

y = -3(1) + 6 – 24

y = -3 + 6 – 24 = -21, meaning that the maximum value of this quadratic function is -21

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

take the derivative

and set = zero

y'=-6x-6 = 0

6x=-6

x=-6/6=-1

solve for x

x=-1 at the maximum y value

plug into the original equation

y=-3(-1)^2 -6(-1) -24

=-3+6-24 = - 21