A soccer ball is kicked into the air, and its path can be modeled with a quadratic function. The table shows the time, t, in seconds, and the height of the soccer ball, h, in feet. Follow the steps to write the function. 1. Identify x-intercepts: (0, 0) and (5, 0) 2. Use factored form: f (t) = a (t - 0) (t - 5) f (t) = at (t - 5) 3. Find the value of: 12 = a (3) (3 - 5) 4. Write function: f (t) = t (t - )

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Mathematics

22 October, 14:53

A soccer ball is kicked into the air, and its path can be modeled with a quadratic function. The table shows the time, t, in seconds, and the height of the soccer ball, h, in feet. Follow the steps to write the function. 1. Identify x-intercepts: (0, 0) and (5, 0) 2. Use factored form: f (t) = a (t - 0) (t - 5) f (t) = at (t - 5) 3. Find the value of: 12 = a (3) (3 - 5) 4. Write function: f (t) = t (t - )

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Answers (2)

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Addison Russell · Answer 1

The y-intercepts are

(0,0) and (5,0)

The equation of the quadratic function is

f (t) = at (t-5)

Solving for a

12 = a (3) (3-5)

a = - 2

The equation of the quadractic function is

f (t) = - 2t (t - 5)

f (t) = - 2t² + 10t

Marlon Leach · Answer 2

-2 and - 5

f (t) = - 2t (t - (-5))