A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=92t-16t^2. What is the

Question

vladimir2022 [97]

3 years ago

14

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=92t-16t^2. What is the

maximum height that the ball will reach? Do not round your answer

Mathematics

2 answers:

nata0808 [166] · Answer 1 · 2022-08-28T12:29:32+03:00

Answer:

132.25 feet

Step-by-step explanation:

Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.

The general form for a quadratic equation is ax² + bx + c,

here a is -16, and b is 92

To find the x coordinate of the vertex, use x = -b/(2a)

We have x = -92/[2(-16)]

x = -92/-32

x= 23/8

Now plug that into the equation to find the y value, which will be the height...

y = 92(23/8) - 16(23/8)²

y = 2116/8 - 16(529/64)

y = 1058/4 - 529/4

y = 529/4

y = 132.25

Brut [27] · Answer 2 · 2022-08-28T14:49:08+03:00

The maximum height that the ball will reach : <u>132.25 ft</u>

<h3>Further explanation </h3>

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

f (x) = ax² + bx + c

where a, b, and c are real numbers and a ≠ 0.

The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value

<em>So the maximum is if a <0 and the minimum if a> 0. </em>

<em />

The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.

The maximum / minimum point of the quadratic function is

$\rm -\dfrac{b}{2a},-\dfrac{D}{4a}$