A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -2x 2 + 8x. At what point does the ball hit the ground?
Accepted Solution
A:
check the picture below. That's about what a parabola for an "initial velocity" case would look like.
anyhow, it hits the ground at two points, when it began, and when it came back down, and that happens when y = 0.
[tex]\bf h(x)=-2x^2+8x\implies \stackrel{h(x)}{0}=-2x^2+8x\implies 0=-2x(x-4)\\\\
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0=-2x\implies 0=x\qquad \impliedby \textit{when it began}\\\\
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0=x-4\implies \boxed{4=x}\qquad \impliedby \textit{when it came back down}[/tex]