the height of a kicked soccer ball is represented by the function f (x) = 8x-2x^2 where x is the number of seconds since the ball was iicked and f (x) is the height of the ball. when will the soccer ball hit the ground?

Result at time x = 4 seconds the soccer ball hit the ground.

Step-by-step explanation:

At the moment just before the ball is kicked, it is on the ground and so the height f (x) is zero meters. After the kick, the ball goes through the air and it's path can be described by a (mountain) parabola.

So lets see after how many second (x) the height = 0 once again.

f (x) = 8x-2x^2

f (x) = 0

8x - 2x^2 = 0

Try to write the formula in two terms

-2x * (x - 4) = 0

When a product of two or more terms equals zero, then at least one of the terms must be zero.

Now solve each term = 0 separately, meaning, solve as many equations as there are terms in the product.

Any solution of term = 0 solves product = 0.

Solve the first term:

-2x = 0

Multiply left an right from the = singn with the factor - 1 gives this outcome:

2x = 0

x = 0

Solve the second term:

x-4 = 0

x = 4

Result at time x = 4 seconds the soccer ball hit the ground.

x = 4

x = 0