A football player throws a football. The function h given by h(t) = 5 + 60 t - 16 t^{2} describes the footballs height in feet t seconds after it is thrown select all the statements that are true about this situation.

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Select all the statements that are true about this situation.


The football is thrown from ground level.


The football is thrown from 5 feet off the ground.


In the function,  -16 t^{2} represents the effect of gravity.


The outputs of h decrease then increase in value.


The function h has 2 zeros that make sense in this situation.


The vertex of the graph of h gives the maximum height of the football.

Sangeetha Pulapaka

Options B, C and F are the correct options.

  • The linear expression 5 + 60 t represents the height the object would have at time t, if there were no gravity. The object would keep going up at the same speed at which it was thrown. The graph would be a line with a slope of 60 which relates to the constant speed of 60 feet per second.
  • The expression -16t^{2} represents the effect of gravity, which eventually causes the object to slow down, stop, and start falling back again.
  • The vertex of the graph (h, k) represents the highest/lowest point of a parabola. Since we have a negative sign, it means that the parabola opens down, and so we have a maximum point.