Question

I'll fan and medal :) A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? I keep getting the wrong answer. Someone help walk me through it?

Answer 1

\[-16t^2 +48t = -16t(t-3)\]
setting equal to 0 gives t =0,3

this means that the ball hits the ground after 3 sec, the axis of symmetry is a vertical line that goes through the vertex(max) of parabola. The vertex is always half-way between the zeroes(x-intercepts)

midpoint of 0 and 3 is 1.5
axis of symmetry --> t = 1.5