Hurry. A catapult launches a pumpkin with an upward velocity of 150 ft./s.
The height of the pumpkin, h, in feet after t seconds is given by the
function h = -16t2 + 150t + 20. How long does it take the
pumpkin to reach its maximum height? What is the pumpkin's
maximum height? Round to the nearest hundredth, if necessary.

Time taken to reach maximum height=4.69 seconds

Maximum Height=371.56feet

Step-by-step explanation:

Given the height function of the pumpkin:

The pumpkin reaches it's maximum height at its axis of symmetry.

Therefore, we determine its equation of symmetry.

The equation of symmetry:

a=-16, b=150.

Therefore:

The pumpkin reaches maximum height after 4.6875 seconds.

At t=4.6875

The pumpkin's maximum height is 371.56 feet.

d. vertex

step-by-step explanation:

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: