Question

Just need help with this one real quick. What do I put for B.I know the maximum value is (3,24)

Answer 1

We were given:

`\begin{gathered} f(x)=-3x^2+18x-3 \\ f(x)=y \\ \Rightarrow y=-3x^2+18x-3 \\ y=-3x^2+18x-3 \\ a=-3,b=18,c=-3 \end{gathered}`

We will calculate the minimum point as shown below:

`\begin{gathered} min=c-(b^2)/(4a) \\ min=-3-(18^2)/(4(-3)) \\ min=-3-(324)/(-12) \\ min=-3-(-27) \\ min=-3+27 \\ min=24 \\ \text{This is the maximum value (not minimum)} \\ x=-(b)/(2a) \\ x=-(18)/(2(-3)) \\ x=(-18)/(-6) \\ x=3 \\ \\ \therefore Maximum\text{ point is (3, 24)} \end{gathered}`

This quadratic equation opens downward because the value of ''a'' is negative. Hence, the function only has a maximum point, it does not have a minimum point

The maximum value of the function is 24 and it occurs at x equals 3