Cathy hit a golf ball 180 yards down the fairway. If the ball reached a maximum height of 25 yards, what is the equation(in graphing form) for the height of the golf ball versus the horizontal distance it has traveled? Assume a parabolic path.

1 Answer
Somebody N.
Apr 12, 2018

See below.

Explanation:

Let the x axis be the horizontal distance and the y axis be the vertical distance.

We know the ball travelled 180 yards. If we construct a quadratic equation with roots at #x=0# the starting point and #x=180# the final distance, then we just have to make the maximum value of the function #y=25#.

We know the vertex of a parabola has an axis of symmetry midpoint of the roots. We use #(180-0)/2=90# to find this.

Using vertex form of a quadratic:

#y=a(x-h)^2+k#

Where:

#bbacolor(white)(888)# is the coefficient of #x^2#.

#bbhcolor(white)(888)# is the axis of symmetry.

#bbkcolor(white)(888)# is max/min value.

Plugging in what we know, and using one of the roots:

#y=a(0-(90))^2+25#

we now solve for #bba#

First we need a value for #y#. We know at #x=0# the ball is sill on the ground, so we can say at #x=0=>y=0#

So:

#a(0-(90))^2+25=0#

#90^2a+25=0#

#90^2a=-25#

#a=-25/90^2=-1/324#

#:.#

#y=-1/324(x-90)^2+25#

This is the required equation. We can expand this if we need to, so as to have the form #ax^2+bx+c#.

GRAPH:

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