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 the function: f(t) = t(t − )

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HarLit2004 HarLit2004 · Answer 1 · 2020-05-26T23:37:23+02:00

Answer:

First box (-2)

Second Box (5)

Step-by-step explanation:

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raphealnwobi raphealnwobi · Answer 2 · 2022-02-23T12:26:51+01:00

The polynomial that show the relationship between t and h is f(t) = -2t(t - 5)

A polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, quadratic and cubic.

Given the x intercepts at (0, 0) and (5, 0), hence:

t = 0, or t = 5

t = 0 or t - 5 = 0

a(t)(t - 5) = f(t)

at² - 5at = f(t)

at t = 3, f(t) = 12:

a(3)² - 5a(3) = 12

a = -2

-2t² + 10t = f(t)

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

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