A football player kicks a football downfield

Question

A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 20 yards, 35 yards away from the player. A second kick is modeled by f(x)=-0.051x(x-50), when f is the height (in yards) and x s the horizontal distance (in yards). Comare the distances that the footballs travel before hitting the ground.

Was the first or second kick travel father before hitting the ground

How much did the kick travel (in yards) farther.

Answer 1

Hi Larissa - First thing to keep in mind here is that both footballs travel in a parabola and for ease of calculations, we assume that they are kicked from the vertex on the coordinate plane (height is zero and distance is zero so point (0,0) ).

You are given the equation for the second football but not the first. If you want to use the equation for the first football, you would need to generate that equation from the vertex formula (y=a(x-x₀ )² +y₀ ) ,the vertex (max height point or (35,20) and the starting point (0,0). However, you do not really need to do that unless you are a very visual learner and really want to graph the 2 parabolas.

Key points to get a solution ....

for football one, a parabola is symmetric so the football takes the same time/distance to come as down as it did to come up.

for football two, if you set f(x) = 0 you will get the two zeros or roots. Those are the two locations that the ball is on the ground (height = 0). One root will be (0,0) the starting point. The other root will be where the ball landed.