SOLUTION: HELP!!! tonisha hit a ball into the air with an initial velocity of 48 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t squared+48t+2,

Question 85825: HELP!!!
tonisha hit a ball into the air with an initial velocity of 48 feet per second. the height h in feet of the ball above the ground can be modeled by h=-16t squared+48t+2, where t is the time in seconds after tonisha hit the ball. find the time it takes the ball to reach 38 feet above the ground.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The problem tells you that the equation for the height of the ball is:
.

.
It asks you to find the time that the ball reaches a height of 38 feet.
.
Substitute 38 feet into the equation. Since 38 feet is the height, it replaces h in the
equation, and the equation becomes:
.

.
The standard form for solving equations of this type is:
.

.
in which a, b, and c are integers.
.
You can work the height equation into this form. Begin by transposing (switching sides) of
the height equation to get:
.

.
Next subtract 38 from both sides of the equation:
.

.
and after the subtraction the left side becomes:
.

.
Notice that this equation now matches the standard form ... in which a = -16, b = +48, and
c = -36.
.
You can simplify this a little by noting that 4 is a factor of all the terms. So divide
all the terms in this equation by 4 to get:
.

.
You can further simplify this by multiplying all the terms on both sides by -1 to get:
.

.
This can be solved by using the quadratic formula, or you might notice that the left side
of this equation factors to give:
.

.
The equation will be true when the left side equals zero. Therefore, it will be true if

.
Solve this equation by adding 3 to both sides to get:
.

.
and solve for t by dividing both sides by 2 to get:
.
seconds.
.
So the ball reaches a height of 38 feet 1.5 seconds after Tonisha hits it.
.
Hope this helps you to understand the problem.

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