Question

A football is kicked forward the goal. The height of the ball is modeled by the function h(t) = -16t2 + 64t 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?

A.) t=2; it takes 2 seconds to reach the maximum height in 2 seconds to fall back to the ground

B.) t=2; it takes 2 seconds to reach the maximum height in 4 seconds to fall back to ground

C.) t=4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground

D.) t=4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground

Answer 1

check the first picture below, that's pretty much the trajectory of an object under the effect of gravity.

check the second picture below.

so the ball goes up up, reaches the vertex and then down down, what is the x-coordinate of the vertex anyway?


`\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{64}{2(-16)}~~,~~\qquad \right)\implies \left(-\cfrac{64}{-32}~~,~~\qquad \right)\implies (2~,~)`

the ball goes up up, reaches a maximum height in 2 seconds, then takes another 2 seconds falling back down.