A soccer ball was kicked in the air and follows the path h(x)=−2x2+1x+6, where x is the time in seconds and h is the height of the soccer ball. At what time will the soccer ball hit the ground

The ball will hit the ground at 2 seconds.

Step-by-step explanation:

Given that,

The path of the ball = h(x)=−2x2+1x+6

Here,

x is the time while h is the height of ball.

When the ball will hit the ground, the height will become zero. Therefore,

h(x)=−2x2+1x+6

0 =−2x2+1x+6

or

2x2 -1x - 6 = 0

This is a quadratic equation, hence by applying quadratic equation formula:

here,

a = 2

b = -1

c = -6

Putting these values in formula, we get

x = 2, -3/2

As the time cannot be negative. Therefore, the ball will hit the ground at 2 seconds.

2 seconds

Step-by-step explanation:

The equation that models the height of the soccer ball is

When the soccer ball hit the ground, then the height is zero.

This implies that:

We split the middle term to get:

We factor to get:

Since time must be positive, we have x=2