Question

The path of a ball kicked from the ground can be modeled by the equation y=−1/3(x−3)(x−21), where x and y are measured in feet. The x-axis represents the ground. How far does the ball land from where it is kicked?


The ball lands

feet from where it is kicked.

Answer 1

Answer:

The ball lands  18 feet from where it is kicked.

Step-by-step explanation:

Given : The path of a ball kicked from the ground can be modeled by the equation $y=-\frac{1}{3}(x-3)(x-21)$, where x and y are measured in feet. The x-axis represents the ground.

To find : How far does the ball land from where it is kicked?

Solution :

According to question,

The value of y is zero as it is kicked from ground.

So, $0=-\frac{1}{3}(x-3)(x-21)$

Applying zero product property,

$a\cdot b\cdot c=0\Rightarrow a=0\text{ or }b=0\text{ or }c=0$

i.e. $-\frac{1}{3}\cdot (x-3)\cdot (x-21)=0$

$x-3=0$

$\Rightarrow x=3$

$\text{ or }x-21=0$

$\Rightarrow x=21$

The distance the ball land from where it is kicked is d=21-3=18.

Therefore, the ball lands  18 feet from where it is kicked.