13.
(a)
[tex]y=-5x^2+21x-3[/tex]
for x = 2:
[tex]y=-5(2)^2+21(2)-3=-20+42-3=19[/tex]
for x = 5
[tex]y=-5(5)^2+21(5)-3=-125+105-3=-23[/tex]
(b)
The graph is:
(c)
Using the graph:
[tex]\begin{gathered} x=1.8,y=18.6 \\ x=0.548,y=7 \\ x=3.65,y=7 \end{gathered}[/tex][tex]\begin{gathered} x=1.8 \\ y=-5(1.8)^2+21(1.8)-3=-16.2+37.8-3=18.6 \end{gathered}[/tex][tex]\begin{gathered} y=7 \\ -5x^2+21x-3=7 \\ -5x^2+21x-10=0 \end{gathered}[/tex]
Using the quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-21\pm\sqrt[]{21^2-4(-5)(-10)}}{2(-5)} \\ x=\frac{-21\pm\sqrt[]{241}}{-10} \\ x=0.54758 \\ or \\ x=3.6524 \end{gathered}[/tex]
