Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

The height $ y $ (in feet) of a punted football is given by

$ y = - \frac{16}{2025} x^2 + \frac{9}{5} x + 1.5 $

where $ x $ is the horizontal distance (in feet) from the point at which the ball is punted.

(a) How high is the ball when it is punted?(b) What is the maximum height of the punt?(c) How long is the punt?

a) 1.5 feetb) $\frac{6657}{64}$c) $\frac{45}{32}(81+\sqrt{6657})$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Campbell University

McMaster University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

06:07

HEIGHT OF A BALL The heigh…

04:15

The height $y$ (in feet) o…

04:52

Football A football player…

02:12

The height of a ball throw…

02:14

A baseball player throws a…

04:13

A ball is thrown upward an…

03:41

08:04

Jim kicks a football from…

Maximum Height of a Footba…

06:54

Path of a Ball A ball is t…

so the height in feet of a punching ball is given by this equation. Here, skip just a little rough sketch of what's going on So originally by plugging in X equals zero before the ball is punted, we find the initial height of the ball one point five, and we can see that this is a parable of that opens downwards. So more or less we're getting a graph that looks like this and there's a few pieces of information will want. One is we want the backside. So if we call the Vertex H K, then the max, I will be the K value. And also we see that this right most X intercept is the horizontal length of the pun. So let's start answering questions. A through C So for parquet, How high is the ball when the ball is punted? This's just why of zero, which we saw as one point five by plugging in X equals zero here one point five feet. So Part B, we want the max height of the pun. So as we mentioned, we want the white corner of the verse six. So we'LL use the fact that the verse X could also be written as negative B over two A and then f of negative B over two a or here, I mean, in general FX X squared plus B x X plus seat. So first we should go ahead and find the value negative B over two A. So here we see are a value in front of the X Square and we see are the value so negative B over two A. You go ahead and simplify that in a copulate. Er, you get this fraction over here. Three, six, four, five over thirty two. And then the next step would be to go ahead and plug that X value that you get back into the formula. So now we plug in this fraction. Over here, we plug in for X and the original formula. And when you do that, get this expression over here. So this is the original. Why? Value and I've plugged in the X value that we found the negative B over two A. And you get six, six, five, seven over sixty four. So that's the K value. That's the max height. Okay, we have one more part here. This is the length of the punt. So you can see here the length of the paan is just an eccentric set. So if we could just find this X value here, that will be the length of the pun. So we're dealing with the quadratic, and we know that these things may have two X intercepts. If you look at our graph, if we continue to the left, you can see that this would have a negative X intercept. But that's not what we want here. So we have to make sure we're choosing the right value. You can see that this left most ex intercept is negative, so that would not make any sense here. So we just want the positive value, the positive X intercept. So what you can do here is just used the quadratic formula. So in general, we'd use this formula here where this is our eh, that's R B. And then one point five is our sea. And when we do that, plugging these in for a B and C and using the minus sign. So if you use the minus in front of the square room, you get this value two to eight point six four However, if you use the plus sign, then you'LL get the negative X intercept that we were talking about. So we do not want that value and therefore will stick with the positive value. And that rounds out to about two. Twenty eight point six four. And that results Percy.

View More Answers From This Book

Find Another Textbook

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

HEIGHT OF A BALL The heighty (in feet) of a punted football is given by …

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

Football A football player punts a ball. The path of the ball can be modeled…

The height of a ball thrown across a field, $f(x),$ in feet, can be modeled …

A baseball player throws a ball, and the height of the ball (in feet) can be…

A ball is thrown upward and outward from a height of 6 feet. The height of t…

Jim kicks a football from the ground with an initial velocity of 140 feet p…

Maximum Height of a Football If a football is kicked straight up with an ini…

Path of a Ball A ball is thrown across a playing field from a height of 5 $\…

01:28

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

05:35

Let $ P(x_1, y_1) $ be a point on the hyperbola $ x^2/a^2 - y^2/b^2 = 1 $ wi…

04:16

In Exercises 93 - 96, use the Intermediate Value Theorem and the tab…

02:24

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

01:57

In Exercises 65 - 74, find a polynomial of degree $ n $ that has the given …

03:44

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

03:15

Solve the initial-value problem.

$ 9y" + 12y' + 4y = 0 $, …

01:33

Solve the differential equation.

$ 4y'' + 4y' + y = 0…

01:38

Fill in the blanks.

A polynomial function of degree and leading coef…

01:17

In Exercises 105 - 107, determine whether the statement is true or false. Ju…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.