Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The path of a diver is given by

$ y = - \frac{4}{9} x^2 + \frac{24}{9} + 12 $

where $ y $ is the height (in feet) and $ x $ is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?

16

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Missouri State University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

02:05

The path of a diver is app…

01:50

The path of a diver diving…

01:53

An object is projected so …

01:00

03:27

A wire is attached to the …

03:17

An object projected from t…

01:34

Water from an outdoor foun…

01:24

A sprinkler set at ground …

01:10

A boat is being pulled tow…

01:59

Height of a Ball If a ball…

00:50

02:02

For the object from the pr…

02:16

01:54

Architecture. A parabolic …

04:15

The height $y$ (in feet) o…

01:38

A rocket is launched in th…

02:13

01:17

Maximizing height. A ball …

03:00

A child kicks a ball a dis…

01:14

A stone is launched vertic…

So here we have the path of a diver is given by this parable equation. Why is height and feet and X is the horrid on horizontal distance from the diving board? So the diving board, if you plug in X, equals zero, you see that the diving more is twelve feet high, the person jumps off. And then before they come back down, they reached the Vertex, and we want to know the Y values of the vortex. So that's what we're looking for, the K actually here. It's not necessary to do the standard form. You can use the fact that the birth hicks for a proble is always given by the point where this is coming from the standard form or they're just the original form of ah, quadratic. So this is the value that we want here. First, we need to plug in negative B over two A. So in our problem, we can see that B. It's twenty four over nine and we see that a He's negative for over nine ssa plugging this in. I could cancel those minus signs. You could also cancel those nines and I'LL give you twenty for over eight which equals three. So now we want this value here. So just plug in three and four X. And so our function. So you get negative for over nine times three squared, plus twenty for over nine times three and then plus twelve. We could cancel those. Nice. So here we have cancel three. Twenty for over three years. Eight. Tow us. Write this out. We have negative for plus eight. Closed twelve, and that simplifies to sixteen feet. That is the maximum height of the diver.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

The path of a diver is approximated by $y=-\frac{4}{9} x^{2}+\frac{24}{9} x+…

The path of a diver diving from a 10 -foot high diving board is$$h=-…

An object is projected so as to follow a parabolic path given by $y=-x^{2}+9…

A wire is attached to the top of a pole. The pole is $2 \mathrm{ft}$ shorter…

An object projected from the ground at a 45 degree angle with initial veloci…

Water from an outdoor fountain is projected outward from a jet on the side w…

A sprinkler set at ground level shoots water upward in a parabolic arc. If t…

A boat is being pulled toward a dock with a rope attached at water level. Wh…

Height of a Ball If a ball is thrown directly upward with a velocity of 40 $…

Height of a Ball If a ball is thrown directly upward with a velocity of $40 …

For the object from the previous exercise, assume the path followed is given…

Architecture. A parabolic arch has an equation of $x^{2}+20 y-400=0,$ where …

The height $y$ (in feet) of a punted football is approximated by $y=-\frac{1…

A rocket is launched in the air. Its height, in meters, above sea level, as …

A rocket is launched in the air. Its height, in meters above sea level, as a…

Maximizing height. A ball is thrown straight up from the top of a building $…

A child kicks a ball a distance of 9 feet. The maximum height of the ball ab…

A stone is launched vertically upward from a cliff 192 feet above the ground…

01:33

Solve the differential equation.

$ 4y'' + 4y' + y = 0…

01:28

In Exercises 89 - 92, use a graphing utility to graph the function.…

01:03

Fill in the blanks.

If the graph of a quadratic function opens upwar…

04:35

In Exercises 35-42, use a graphing utility to graph the quadratic function. …

03:05

In Exercises 65-70, find two quadratic functions, one that opens upward and …

$ y'' + 2y = 0 $

00:26

In Exercises 47 - 54, write the function in the form $ f(x) = (x - k)q(x) + …

01:01

Write a polar equation of a conic with the focus at the origin and the given…

In Exercises 31- 34, use a graphing utility to graph the functions …

02:42

In Exercises 9 - 16, match the polynomial function with its graph. [The grap…