Aball is thrown into the air from a height of 256 feet at time t=0. the function that models this situation is h(t)=-16t^2 + 96t + 256, where t is in seconds and h is the height in feet.

a.) what is the height of the ball at 2 seconds?
b.) when will the ball reach a height of 144 feet?
c.) when will the ball hit the ground?

Part A) The height of the ball at 2 seconds is

Part B)

Part C)

Step-by-step explanation:

Part A) what is the height of the ball at 2 seconds?

we have

so

For

Substitute the value of t in the equation and solve for h

Part B) When will the ball reach a height of 144 feet?

Substitute the value of in the equation and solve for t

so

we know that

The formula to solve a quadratic equation of the form is equal to

in this problem we have

so

substitute in the formula

therefore

the solution is the positive value

Part C) When will the ball hit the ground?

Substitute the value of in the equation and solve for t

so

we know that

The formula to solve a quadratic equation of the form is equal to

in this problem we have

so

substitute in the formula

therefore

the solution is the positive value

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: