Explanation Given: The equation of the parabola is x 2 + 6 x = y − 4 . Formula used: The standard form of a vertical parabola with its vertex at ( h , k ) is given by, y = a ( x − h ) 2 + k , where a ≠ 0 Calculation: Consider the equation x 2 + 6 x = y − 4 . Now, As the x term is squared, then, it is a vertical parabola. Keep y on one side and group the x terms along with the constants on the right-hand side, as follows, x 2 + 6 x = y − 4 y = x 2 + 6 x + 4 Then, complete the square of the equation, to get the standard form, y = x 2 + 6 x + 4 = x 2 + 2 ⋅ 3 x + 9 &#

MyLab Math with Pearson eText -- 24 MonthStandalone Access Card -- for Intermediate Algebra with Integrated Review

8th Edition

ISBN: 9780135910023

Author: Tobey, John, Slater, Jeffrey, Blair, Jamie , Crawford, Jenny

Publisher: PEARSON

See similar textbooks

Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Videos

Question

Chapter 9, Problem 10RP

To determine

To calculate: The vertex and direction in which the parabola opens given by the equation x2+6x=y−4 and rewrite in its standard form.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 9RP

Chapter 9, Problem 11RP

Students have asked these similar questions

How long will it take you to double your money if you invest it at a rate of 8% compounded annually?

One hundred dollars is invested at 7.2% interest compounded annually. Determine how much the investment is worth after: a. I year b. 5 years c. 10 years d. 20 years e. Use your answers to parts (a)-(d) to estimate the doubling time for the investment.

6) A farmer has 60 acres on which to plant oats or corn. Each acre of oats requires 100 lbs of fertilizer and 1 hour of labor. Each acre of corn requires 50 lbs of fertilizer and 2 hours of labor. The farmer has 5000 lbs of fertilizer and 100 hours available for labor. If the profit is $60 from each acre of oats and $100 from each acre of corn, what planting combination will produce the greatest total profit? a) Fill in the following chart to help organize the information given in the problem: Oats Labor Fertilizer Land Profit b) Write down the question of interest. Corn Available c) Define variables to answer the question of interest. Call these x and y. d) Write the objective function to answer the question of interest. e) List any constraints given in the problem.

Chapter 9 Solutions

MyLab Math with Pearson eText -- 24 MonthStandalone Access Card -- for Intermediate Algebra with Integrated Review

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Find the distance between each pair of points....

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Find the distance between each pair of points....Ch. 9.1 - Prob. 17E Ch. 9.1 - Find the two values of the unknown coordinate so...Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 1QQ Ch. 9.1 - Prob. 2QQ Ch. 9.1 - Prob. 3QQ Ch. 9.1 - Prob. 4QQ Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Satellite Dishes Modern satellite dishes intended...Ch. 9.2 - Satellite Dishes Modern satellite dishes intended...Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Prob. 1QQ Ch. 9.2 - Prob. 2QQ Ch. 9.2 - Prob. 3QQ Ch. 9.2 - Prob. 4QQ Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Prob. 34E Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 1QQ Ch. 9.3 - Prob. 2QQ Ch. 9.3 - Prob. 3QQ Ch. 9.3 - Prob. 4QQ Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - Prob. 18E Ch. 9.4 - Prob. 19E Ch. 9.4 - Prob. 20E Ch. 9.4 - Prob. 21E Ch. 9.4 - Prob. 22E Ch. 9.4 - Prob. 23E Ch. 9.4 - Prob. 24E Ch. 9.4 - Prob. 25E Ch. 9.4 - Prob. 26E Ch. 9.4 - Prob. 27E Ch. 9.4 - Prob. 28E Ch. 9.4 - Prob. 29E Ch. 9.4 - Prob. 30E Ch. 9.4 - Prob. 31E Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 1QQ Ch. 9.4 - Prob. 2QQ Ch. 9.4 - Prob. 3QQ Ch. 9.4 - Prob. 4QQ Ch. 9.5 - Prob. 1E Ch. 9.5 - Prob. 2E Ch. 9.5 - Prob. 3E Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Prob. 6E Ch. 9.5 - Prob. 7E Ch. 9.5 - Prob. 8E Ch. 9.5 - Prob. 9E Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Prob. 13E Ch. 9.5 - Prob. 14E Ch. 9.5 - Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - Prob. 17E Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - Prob. 23E Ch. 9.5 - Prob. 24E Ch. 9.5 - Prob. 25E Ch. 9.5 - Prob. 26E Ch. 9.5 - Prob. 27E Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Prob. 30E Ch. 9.5 - Prob. 1QQ Ch. 9.5 - Prob. 2QQ Ch. 9.5 - Prob. 3QQ Ch. 9.5 - Prob. 4QQ Ch. 9 - In exercises 1 and 2, find the distance between...Ch. 9 - Prob. 2RP Ch. 9 - Prob. 3RP Ch. 9 - Prob. 4RP Ch. 9 - Prob. 5RP Ch. 9 - Prob. 6RP Ch. 9 - Prob. 7RP Ch. 9 - Prob. 8RP Ch. 9 - Prob. 9RP Ch. 9 - Prob. 10RP Ch. 9 - Prob. 11RP Ch. 9 - Prob. 12RP Ch. 9 - Prob. 13RP Ch. 9 - Prob. 14RP Ch. 9 - Prob. 15RP Ch. 9 - Prob. 16RP Ch. 9 - Prob. 17RP Ch. 9 - Prob. 18RP Ch. 9 - Prob. 19RP Ch. 9 - Prob. 20RP Ch. 9 - Prob. 21RP Ch. 9 - Prob. 22RP Ch. 9 - Prob. 23RP Ch. 9 - Solve each nonlinear system. If there is no real...Ch. 9 - Prob. 25RP Ch. 9 - Prob. 26RP Ch. 9 - Prob. 27RP Ch. 9 - Prob. 1T Ch. 9 - Prob. 2T Ch. 9 - Rewrite the equation in standard form. Identify...Ch. 9 - Prob. 4T Ch. 9 - Prob. 5T Ch. 9 - Prob. 6T Ch. 9 - Prob. 7T Ch. 9 - Prob. 8T Ch. 9 - Prob. 9T Ch. 9 - Prob. 10T Ch. 9 - Prob. 11T Ch. 9 - Prob. 12T Ch. 9 - Prob. 13T Ch. 9 - Prob. 14T Ch. 9 - Prob. 15T Ch. 9 - Prob. 16T

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The vertex and direction in which the parabola opens given by the equation x 2 + 6 x = y − 4 and rewrite in its standard form.

Solution Summary: The author calculates the vertex and direction in which the parabola opens by the equation x2+6x=y-4 and rewrites in its standard form.

Concept explainers

Videos

To calculate: The vertex and direction in which the parabola opens given by the equation x2+6x=y−4 and rewrite in its standard form.

Want to see the full answer?

Chapter 9 Solutions