finding the zeros of a quadratic function - The equation y = (-16t -2)(t-1) represents the height in feet of a beach ball thrown by a child as a function of time, t, in seconds.

Sangeetha Pulapaka (last edited 1 year ago) (Expert, Educator @Qalaxia)

1) The zeros of the function y = (-16 t - 2)(t-1) can be found by plugging in y = 0, to get (-16 t - 2)(t -1) = 0

\Rightarrow -16 t - 2 = 0 and t - 1 = 0

\Rightarrow t = \frac{-2}{16} = \frac{-1}{8} and t = 1.

So 1, -1/8 are the zeros of the function.

2) It is given that the height of the ball, in feet, is a function of time, t, in seconds. So time lies on the x-axis and the height lies on the y-axis (1,0) says that when the time is 1 second the height of the beachball is 0. Negative value of zero is not realistic in this situation because time in seconds cannot be a negative value. So t = 1 is the only meaningful zero.

3) This can be found by finding the y-intercept of the given function. We plug in t = 0 in the given equation to find the height at which the beach ball is thrown.

Given

y = (-16 t -2)(t-1)

Plugging in t = 0,

y = (-2)(-1) = 2

So when the time is zero, the height of the beachball is 2 feet. The ball was thrown from a height of 2 feet.