[tex]g(x)=-2x^2+20x-52[/tex][tex]\begin{gathered} g(x)=ax^2+bx+c \\ \\ \text{Maximum:} \\ a<0 \\ \\ \text{Minimum:} \\ a>0 \end{gathered}[/tex]
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:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ \\ x=-\frac{20}{2(-2)}=-\frac{20}{-4}=5 \end{gathered}[/tex]
2. Evaluate the value of the function when x=5
[tex]\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}[/tex]
Then, the function's maximum value is -2
the maximum value occur when x= 5
