Question

Determine without graphing whether the given quadratic function had a maximum value or a minimum value and then find the value. F(x)=3x^2+12x-4Is this equation minimum or maximum? Also what is the value?

Answer 1

Given function:

`f(x)=3x^2+12x-4`

a = 3

As a is positive the parabola opens upward. It has a minimum value.

To find the minimum:

1. Find the value of x where the parabola has the minimum value, use the next formula:

`\begin{gathered} x=-(b)/(2a) \\ \\ x=-(12)/(2(3))=-(12)/(6)=-2 \end{gathered}`

2. Use the value of x where the function has minimum value (step 1) to find the value of the function:

`\begin{gathered} f(-2)=3(-2)^2+12(-2)-4 \\ f(-2)=3(4)-24-4 \\ f(-2)=12-24-4 \\ f(-2)=-16 \end{gathered}`Then, the minimum value of the given function is -16 (f(-2)=-16)