Question

Answer the questions below about the quadratic function.g(x) = 2x² + 20x - 52Does the function have a minimum or maximum value?MinimumMaximumWhat is the function's minimum or maximum value?Where does the minimum or maximum value occur?

Answer 1

`g(x)=-2x^2+20x-52`
`\begin{gathered} g(x)=ax^2+bx+c \\ \\ \text{Maximum:} \\ a<0 \\ \\ \text{Minimum:} \\ a>0 \end{gathered}`

In the given function g(x) has a= -2 (a< 0) it has a maximum.

To find the maximum value:

1. Find the value of x in the vertex:

`\begin{gathered} x=-(b)/(2a) \\ \\ x=-(20)/(2(-2))=-(20)/(-4)=5 \end{gathered}`

2. Evaluate the value of the function when x=5

`\begin{gathered} g(5)=-2(5)^2+20(5)-52 \\ g(5)=-2(25)+100-52 \\ g(5)=-50+100-52 \\ g(5)=-2 \end{gathered}`

Then, the function's maximum value is -2

the maximum value occur when x= 5