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Emily threw a ball up in the air from her tree house. It followed the path given by the parabola y equals short dash 2 x squared plus 14 x plus 60, where x is the distance from the tree house (in feet), and y is the height of the ball (in feet). At what distance from the tree house did the ball strike the ground?

Answer :

Abidemiokingo

The distance from the tree house that the ball strike the ground is 10feet

Equation of a parabola

Given the path of the ball expressed by the parabola equation:

y = -2x^2+14x +60

The point where the ball strikes the ground is the point where y = 0. Substitute into the equation to have:
-2x^2+14x +60 = 0

x^2 - 7x - 30 = 0

Factorize the result

x^2 - 10x + 3x - 30 = 0
x(x-10)+3(x-10) = 0
x - 10 =0

x = 10

Hence the distance from the tree house that the ball strike the ground is 10feet

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