A soccer goalie kicks the soccer ball. The quadratic function y = −16t2 + 64t gives the time t seconds when the soccer ball is at a height 0 feet. How long does it take for the soccer ball to return to the ground?

A polynomial function is a relation where a dependent variable is equal to a polynomial expression. A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.

The highest power to a variable is the degree of the polynomial expression.

When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

How do we solve the given question?

We are given a quadratic function representing the height of the ball after a goalie kicks it. The function is y = −16t² + 64t, where y is the height in feet of the ball at time t seconds.

We are asked how long it takes for the soccer ball to return to the ground.

To calculate the time for the ball to return to the ground, we take height y = 0.

Our equation therefore is,

0 = -16t² + 64t

or, 16t² - 64t = 0

or, t² - 4t = 0

or, t(t-4) = 0

∴ Either, t = 0; Or, t-4 = 0 ⇒ t = 4.

∴ The height of the ball is 0 when time t is 0 and 4. Time 0 is before the goalie kicked the ball, so we take t = 4 seconds.

∴ The ball takes 4 seconds to return to the ground.

Learn more about Quadratic Functions at

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