SOLUTION: At a water fountain, water attains a maximum height of 4m at horizontal distance of 0.5m from its origin. If the path of the water is parabola, find the height of the water at a ho

Question 1170530: At a water fountain, water attains a maximum height of 4m at horizontal distance of 0.5m from its origin. If the path of the water is parabola, find the height of the water at a horizontal distance of 0.75m from the point of origin.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The vertex is at (0.5, 4)
The equation of the parabola in vertex form is f(x)= a(x-h)^2+k
so this is a(x-0.5)^2+4
a known point is at (0, 0)
so a*(0.25)+4=0
.25a=-4
a=-16
can write this as -16x^2+16x.=f(x). This makes sense with gravity and the constant should be 0 if starting at ground level.
check for vertex which is x=0.5 and y=-4+8=4
when x=0.75, f(x)=-9+12=3 feet.

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