Answer:
36
Step-by-step explanation:
We must determine the x and y intercepts of the parabola:
When y=0, x=0 or x=10
WE know that the point of the triangle base is x and x+8. We can substitute this into the parabola equation because the endpoints are on the parabola.
f(x+8)[tex]=-(x^2+16x+64)+10x+80[/tex]
f(x+8)[tex]=-x^2-6x+16[/tex]
f(x)=f(x+8)
[tex]-x^2+10x=-x^2-6x+16[/tex]
solve for x
[tex]16x=16[/tex]
[tex]x=1[/tex]
Therefore the heigh is f(1):
[tex]=-1^2+10=9[/tex]
The area of the triangle is 1/2 base x height:
[tex]=(1/2)\cdot{8}\cdot{9}=36[/tex]
