Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f(x)=−3x2+24x

Question

Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. f(x)=3x²+24x

Answer 1

We define the following two conditions to find the max or min value:

If a>0, then there is a min point

If a<0, then there is a max point

Rewrite the equation:

f(x)=a*x^2+bx

Since a=-3, which is less than 0, then there is a max value.

To find the max value, the x value is defined by -b/2a. So,

x=-24/2(-3)=4

y=f(x)=f(4)=-3*4^2+24*4=48

Therefore, the max point is at (4,48)

I hope this helps. :)