A question about Quadratic Equation.Question:In the TV show Junkyard Wars,a trebuchet was used to catapult a pumpkin from a height of 4 m for a totla horizontal distance of 24 m.It reached a maximum height of 14 m.At what horizontal distances was the

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A question about Quadratic Equation.Question:In the TV show Junkyard Wars,a trebuchet was used to catapult a pumpkin from a height of 4 m for a totla horizontal distance of 24 m.It reached a maximum height of 14 m.At what horizontal distances was the
A question about Quadratic Equation.
Question:In the TV show Junkyard Wars,a trebuchet was used to catapult a pumpkin from a height of 4 m for a totla horizontal distance of 24 m.It reached a maximum height of 14 m.At what horizontal distances was the height of the pumpkin 10 m,to the nearest meter?
Thank you for sigeur's answer.But I was just in grade 10,so I dont know how to solve a EQN system like 4=a(-m)^2+14 and 0=a(24-m)^2+14 .Sorry.
Any way else?
Thank you!:)

A question about Quadratic Equation.Question:In the TV show Junkyard Wars,a trebuchet was used to catapult a pumpkin from a height of 4 m for a totla horizontal distance of 24 m.It reached a maximum height of 14 m.At what horizontal distances was the
From the question give:
1.the y-intercept is 4
2.the x-intercept is 24
3.the y-coodinate of the vertex is 14
We assume the function to be y=a(x-m)^2+14,where a0
give 4=a(-m)^2+14 and 0=a(24-m)^2+14
solve a and m simultanously,
firstly rearrange the equations to
a(-m)^2=-10 and a(24-m)^2=-14
then divide the second equation by the first equation (in order to eliminate "a"),
give (24-m)^2/m^2=7/5
then solve for m,
give m=24/(1+sqrt(7/5))=11,
and a=-0.08275
So y=-0.08275(x-11)^2+14
when y=10,give x=4 or x=18
i.e.at the horizontal distance of 4 meters and 18 meters the height of the pumpkin is 10 meters.

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