Answer:
Given:- [tex]y=-5x^3+10x+20[/tex]
A parabola attain maximum height at the vertex: formula to find x-coordinate of vertex is, [tex]x=-\frac{b}{2a}[/tex]
plug in a=-5 and b=10
so, [tex]x=-\frac{10}{2(-5)} =-\frac{10}{-10} =1[/tex]
Now plug in x=1 to get maximum height,
[tex]y=-5(-1)^2+10(1)+20[/tex]
[tex]=-5+10+20[/tex]
[tex]=+25[/tex]
so, maximum heigh reached by the rocket was 25 yards
Rocket will hit the ground when y=0
[tex]0=-5x^2+10x+20[/tex]
[tex]0=-5(x^2-2x-4)[/tex]
[tex]\frac{0}{-5} =\frac{-5}{-5} (x^2-2x-4)[/tex]
So, [tex]x^2-2x-4=0[/tex]
quadratic formula is,
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
plug in a=1, b=-2,and c=-4
[tex]x=-\frac{(-2)=-\sqrt{(-2)^2-4(1)(-4)} }{2(1)}[/tex]
[tex]=\frac{2=-\sqrt{4+16} }{2}[/tex]
[tex]=\frac{2+-\sqrt{20} }{2}[/tex]
[tex]=\frac{2+-2\sqrt{5} }{2}[/tex]
[tex]=1+-\sqrt{5}[/tex]
[tex]=1-\sqrt{5} ,1+\sqrt{5}[/tex]
[tex]=1-5.236,1+2.236[/tex]
[tex]=-1.236,3.236[/tex]
So, it takes 3.2 seconds to hit the ground.
OAmalOHopeO
