Question

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?​

Answer 1

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

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