Determining the equation

Question

After a football is kicked it reaches a maximum height of 14 meters and it hits the ground 32 meters from where it was kicked.

create an equation that represents the path of the football.

Answer 1

Let h(x) be the height

Let x be the horizontal distance

 

The maximum height occurs at the axis of symmetry of the parabola.  That will be x=32/2=16.  If we put the equation we want in vertex form,

 

h(x) = a(x - 16)² + 14

 

16 meters is half the distance the ball travels.

 

 

The ball hits the ground at 32 meters.  Set h(x) equal to zero and x=32.

 

0 = a(32 - 16)² + 14

 

 

Solve for a.

 

0 = 16²a + 14

 

-14 = 256a

 

(-14/256) = a

 

 

Therefore, your equation is

 

h(x) = (-14/256)(x - 16)² + 14

 

h(x) = (-14/256)(x² - 32x + 256) + 14

 

h(x) = (-14/256)x² + (7/4)x