/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 57 Complete the square and write th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 57

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x-2 y-8=0$$

Short Answer

Expert verified
The equation in standard form is \( (x + 4)^{2} + (y - 1)^{2} = 25 \). Center of the circle is (-4, 1) and the radius is 5.

Step by step solution

01

Group the x and y terms together

First, let's group the x and y terms in the equation together. The equation \( x^{2}+y^{2}+8 x-2 y-8=0 \) becomes \( (x^{2} + 8x) + (y^{2} - 2y) = 8 \)
02

Complete the square for x and y

Completing the square involves adding the square of half of the coefficient of x and y to both sides. This gives the equation \( (x^{2} + 8x + 16) + (y^{2} - 2y + 1) = 8 + 16 + 1 \), which simplifies to \( (x + 4)^{2} + (y - 1)^{2} = 25 \)
03

Identify the center and radius of the circle

In the equation \( (x - h)^{2} + (y - k)^{2} = r^{2} \), (h, k) are the coordinates of the center of the circle, and r is the radius. From our equation \( (x + 4)^{2} + (y - 1)^{2} = 25 \), we can deduce that the center of the circle is (-4, 1) and the radius is 5
04

Graph the equation

When graphing the equation, start by marking the center of the circle at the point (-4, 1). Then, draw a circle with radius 5 around this point.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Begin by graphing the absolute value function, \(f(x)-|x| .\) Then use transformations of this graph to graph the given function. $$ h(x)-2|x+3| $$

Furry Finances A pet insurance policy has a monthly rate that is a function of the age of the insured dog or cat. For pets whose age does not exceed \(4,\) the monthly cost is \(\$ 20\). The cost then increases by \(\$ 2\) for each successive year of the pet's age. $$\begin{array}{|c|c|}\hline\hline\text { Age Not Exceeding } & \text { Monthly Cost } \\\\\hline 4 & \$ 20 \\\5 & \$ 22 \\\6 & \$ 24\end{array}$$ The cost schedule continues in this manner for ages not exceeding \(10 .\) The cost for pets whose ages exceed 10 is S40. Use this information to create a graph that shows the monthly cost of the insurance, \(f(x)\), for a pet of age \(x,\) where the function's domain is \([0,14]\).

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\frac{x^{3}}{2} $$

Write a piecewise function that models each cellphone billing plan. Then graph the function. \(\$ 50\) per month buys 400 minutes. Additional time costs \(\$ 0.30\) per minute.

Describe how to find the inverse of a one-to-one function.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.