What is the equation?

Question

A student estimated based on the video that the ball left my hand 1.65 meters off the ground, and after 0.58 seconds the ball reached the maximum height of 3.26 meters.Use this information to find an equation of the form  for the height of the ball, in meters, after t seconds.

Answer 1

The maximum height is at the vertex. From the given info this will be at (.58,3.26) so equation in vertex form is

y= a(t-.58)^2 + 3.26

at time zero height is 1.65 so we have the point (0,1.65) which we can use to solve for a

1.65= a(0-.58)^2 + 3.26

-1.61=a(.58)^2

a= -1.61/(.58)^2

a= -4.876 so equation is

y= -4.876(x-.58)^2 + 3.26

You can graph this equation to confirm