A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t^2 + 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?

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A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t^2 + 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?

Good evening.The simetry axis can be found with the vertex in x formula:[tex]\mathsf{x_V = -\dfrac{b}{2a}}[/tex]Whe take from the function:a = -16b = 48So:[tex]\mathsf{t_v = -\dfrac{48}{2\cdot (-16)}}\\ \\ \mathsf{t_v = \dfrac{-48}{-32}}\\ \\ \\ \boxed{\mathsf{t_v = \dfrac{3}{2}}}[/tex]We can conclude that the axis of simetry is the line with the equation:t = 3/2It represents that if we take two points at the same x-distance to this line, they will have the same image(value in h).For example:t' = 3/2 + 1/2 = 4/2 = 2t'' = 3/2 - 1/2 = 2/2 = 1We calculate h(t):[tex]\mathsf{h(x') = -16.{1}^2+48.1}\\ \\ \mathsf{h(x') = -16 + 48 = 32}\\ \\ \\ \mathsf{h(x'') = -16.2^2 + 48.2}\\ \\ \mathsf{h(x'')=-64 + 96=32} [/tex]Where we can se the same h-value.Doubts? Please, comment :)

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