Question

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Answer 1

Thus, at x=2 seconds, the ball will hit the ground

Explanation:

Numerical Value of Functions

For any given function h(x) the independent variable x can have any value that belongs to the function domain, and they produce corresponding values for h.

The soccer ball kicked in the air has a function for the path given by

`h(x)=-2x^2+1x+6`

where x is the time in seconds and h is the height of the soccer ball.

The question asks for what time will the soccer ball hit the ground, or find the values of x such as

`h(x)=0`

or equivalently

`-2x^2+1x+6=0`

Factoring

`(x-2)(-2x-3)=0`

The only valid solution is

x=2 seconds

The other solution yields a negative time

Thus, at x=2 seconds, the ball will hit the ground