Suppose a golf ball is driven so that it travels a distance of 400 feet as measured along the ground and reaches an altitude of 300 feet. if the origin represents the tee and is the ball travels along a parabolic path over the positive x-axis, find an equation for the path of the golf ball. which form does the equation fit?

y = [ -3 /400 ] ( x - 200 )^2 + 300

Explanation:

Suppose a golf ball is driven so that it travels a distance of 400 feet as measured along the ground and reaches an altitude of 300 feet. If the origin represents the tee and is the ball travels along a parabolic path over the positive x-axis, find an equation for the path of the golf ball. Which form does the equation fit?

The given question tells us that our vertex is point (h,k), where h is the midpoint of the given horizontal i.e. 400/2 = 200, thus h=200 (horizontal) and k=300 (vertical). So we know we have two zeros with one x at 0 and x at 400.

from the equation of a parabola

y = a ( x - h )^2 + k. substituting the  values and solving to obtain a we have.

y = a (x - 200)^2 + 300

make a the subject of the equation

a = [ y-300 ] / [ ( x - 200)^2 ].

Now for y=0, x =400, thus we have\

a = [ 0 - 300 ] / ( 400 - 200 ) ^2, therefore

a = ( -300 ) / (200^2),

since

a = - 3 / 400.

So finally we have our equation reading as

y = [ -3 /400 ] ( x - 200 )^2 + 300.

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