Question

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 −)

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

Answer 2

The quadratic equation for the soccer ball kicked into the air is,

$f(t) = -2t^2+ 5t$

Given-

Given that t is the time and h is height gain by the ball after kicked.Step 1- Identify x-intercepts at (0,0) and (5,0)

Equation of quadratic function for the given question can be written as,

$y=a(x-h)^2+k$

• Step 1- Identify x-intercepts at (0,0) and (5,0)

The intercepts of y are (0,0) and (5,0)

• Step 2- The equation of the quadratic function

$f(t)= at (t-5)$

• Step 3- Find the value of a for the given function,

$12=a(3)(3-5)$

$12=3a\times(-2)$

$a=\dfrac{12}{-6}$

• Step 4-Function of the equation

Put the value of a in function, we get

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

$f(t) = -2t^2+ 5t$

Hence, the above equation is the required equation for the given problem.

For more about the quadratic function, follow the link below-

https://brainly.com/question/2279619