## Chapter4 Test Algebra 2 Answers Mcdougal

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## Algebra Lesson 6 4 Practice B Answers

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## Using The Quadratic Formula 34 Exercises

**Vocabulary and Core Concept Check**Question 1.**COMPLETE THE SENTENCE**When a, b, and c are real numbers such that a 0, the solutions of the quadratic equation ax2 + bx + c = 0 are x= ____________.Answer:

Question 2.**COMPLETE THE SENTENCE**You can use the ____________ of a quadratic equation to determine the number and type of solutions of the equation.Answer:

5×2 10x 35 = 0Answer:

**ERROR ANALYSIS** In Exercises 33 and 34, describe and correct the error in solving the equation.Question 33.

Question 34.Answer:

**OPEN-ENDED** In Exercises 3540, find a possible pair of integer values for a and c so that the quadratic equation has the given solution. Then write the equation.Question 35.ax2 + 4x + c = 0 two imaginary solutionsAnswer:

ax2 + 6x + c = 0 two real solutionsAnswer:

ax2 8x + c = 0 two real solutionsAnswer:

ax2 6x + c = 0 one real solutionAnswer:

ax2 + 10x = c one real solutionAnswer:

4x + c = ax2 two imaginary solutionsAnswer:

**USING STRUCTURE** In Exercises 4146, use the Quadratic Formula to write a quadratic equation that has the given solutions.Question 41.x = \Answer:

x = \Answer:

x = \Answer:

x = \Answer:

x = \Answer:

x = \Answer:

**COMPARING METHODS** In Exercises 4758, solve the quadratic equation using the Quadratic Formula. Then solve the equation using another method. Which method do you prefer? Explain.Question 47.

**MATHEMATICAL CONNECTIONS** In Exercises 59 and 60, find the value for x.Question 59.Area of the rectangle = 24 m2Answer:

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## Quadratic Equations And Complex Numbers Cumulative Assessment

Question 1.The graph of which inequality is shown?A. y2> x2 + x 6B. y x2 + x 6C. y > x2 x 6D. y x2 x 6Answer:

Classify each function by its function family. Then describe the transformation of the parent function.a. g = x + 4d. g = x + 3 9e. g = \2 1f. h = 6x+ 11Answer:

Question 3.Two baseball players hit back-to-back home runs. The path of each home run is modeled by the parabolas below, where x is the horizontal distance from home plate and y is the height above the ground. Choose the correct symbol for each inequality to model the possible locations of the top of the outfield wall.Answer:

Question 4.You claim it is possible to make a function from the given values that has an axis of symmetry at x = 2. Your friend claims it is possible to make a function that has an axis of symmetry at x = 2. What values can you use to support your claim? What values support your friends claim?Answer:

Which of the following values are x-coordinates of the solutions of the system?y = x2 6x + 14Answer:

Question 6.The table shows the altitudes of a hang glider that descends at a constant rate. How long will it take for the hang glider to descend to an altitude of 100 feet? Justify your answer.A. 25 seconds

## Glencoe Algebra 2 Worksheet

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## Quadratic Equations And Complex Numbers Mathematical Practices

Mathematically proficient students recognize the limitations of technology

**Monitoring Progress**

Question 1.Explain why the second viewing window in Example 1 shows gaps between the upper and lower semicircles, but the third viewing window does not show gaps.Answer:

Use a graphing calculator to draw an accurate graph of the equation. Explain your choice of viewing window.Question 2.y = \Answer:

Answer:

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## Lesson 34 Using The Quadratic Formula

**Essential Question** How can you derive a general formula for solving a quadratic equation?

**EXPLORATION 1**

Deriving the Quadratic FormulaWork with a partner. Analyze and describe what is done in each step in the development of the Quadratic Formula.

**EXPLORATION 2**

Work with a partner. Use the Quadratic Formula to solve each equation.a. x2 4x + 3 = 0b. x2 2x + 2 = 0c. x2 + 2x 3 = 0d. x2 + 4x + 4 = 0e. x2 6x + 10 = 0f. x2 + 4x + 6 = 0

**Communicate Your Answer**

How can you derive a general formula for solving a quadratic equation?Answer:

Question 4.Summarize the following methods you have learned for solving quadratic equations: graphing, using square roots, factoring, completing the square, and using the Quadratic Formula.Answer:

**Solve the equation using the Quadratic Formula.**Question 1.

Answer:

Question 13.Find a possible pair of integer values for a and c so that the equation ax2 + 3x + c = 0 has two real solutions. Then write the equation.Answer:

Question 14.**WHAT IF?**The ball leaves the jugglers hand with an initial vertical velocity of 40 feet per second. How long is the ball in the air?Answer:

## Mcdougal Littell Texas Algebra 2

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## Mcdougal Littell Algebra 2 Answers

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## Big Ideas Math Book Algebra 2 Answer Key Chapter 3 Quadratic Equations And Complex Numbers

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Question 15.**ABSTRACT REASONING**Determine the possible integer values of a and c for which the trinomial ax2+ 8x+c is factorable using the Perfect Square Trinomial Pattern. Explain your reasoning.Answer:

## Lesson 35 Solving Nonlinear Systems

**Essential Question** How can you solve a nonlinear system of equations?

**EXPLORATION 1**

Solving Nonlinear Systems of EquationsWork with a partner. Match each system with its graph. Explain your reasoning. Then solve each system using the graph.

**EXPLORATION 2**

Solving Nonlinear Systems of EquationsWork with a partner. Look back at the nonlinear system in Exploration 1. Suppose you want a more accurate way to solve the system than using a graphical approach.a. Show how you could use a numerical approach by creating a table. For instance, you might use a spreadsheet to solve the system.b. Show how you could use an analytical approach. For instance, you might try solving the system by substitution or elimination.

**Communicate Your Answer**

How can you solve a nonlinear system of equations?Answer:

Question 4.Would you prefer to use a graphical, numerical, or analytical approach to solve the given nonlinear system of equations? Explain your reasoning.Answer:

**Solve the system using any method. Explain your choice of method.**Question 1.

**USING TOOLS** In Exercises 4348, solve the equation by graphing.Question 43.x2 + 2x = \x2 + 2xAnswer:

2×2 12x 16 = 6×2 + 60x 144Answer:

= x2 + 6x 7Answer:

2×2 16x 25 = 6×2 + 48x + 95Answer:

2 3 = 38Answer:

42 = 1Answer:

Question 49.**REASONING**A nonlinear system contains the equations of a constant function and a quadratic function. The system has one solution. Describe the relationship between the graphs.Answer:

**EXPLORATION 1**

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## Quadratic Equations And Complex Numbers Chapter Review

**3.1 Solving Quadratic Equations **

Question 1.Solve x2 2x 8 = 0 by graphing.Answer:

Solve the equation using square roots or by factoring.Question 2.

Write as a complex number in standard form.Answer:

Question 12.The aspect ratio of a widescreen TV is the ratio of the screens width to its height, or 16 : 9. What are the width and the height of a 32-inch widescreen TV? Justify your answer. Answer:

Question 13.The shape of the Gateway Arch in St. Louis, Missouri, can be modeled by y = 0.0063×2 + 4x, where x is the distance from the left foot of the arch and y is the height of the arch above the ground. For what distances x is the arch more than 200 feet above the ground? Justify your answer.Answer:

Question 14.You are playing a game of horseshoes. One of your tosses is modeled in the diagram, where x is the horseshoes horizontal position and y is the corresponding height . Find the maximum height of the horseshoe. Then find the distance the horseshoe travels. Justify your answer.Answer:

## Lesson 31 Solving Quadratic Equations

**Essential Question** How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?

**EXPLORATION 1**

Matching a Quadratic Function with Its GraphWork with a partner. Match each quadratic function with its graph. Explain your reasoning. Determine the number of x-intercepts of the graph.a. f = x2 2xb. f = x2 2x + 1c. f = x2 2x + 2d. f = x2 + 2xe. f = x2 + 2x 1f. f = x2 + 2x 2

**EXPLORATION 2**

Solving Quadratic EquationsWork with a partner. Use the results of Exploration 1 to find the real solutions of each quadratic equation.a. x2 2x = 0b. x2 2x + 1 = 0c. x2 2x + 2 = 0d. x2 + 2x = 0e. x2 + 2x 1 = 0f. x2 + 2x 2 = 0

**Communicate Your Answer**

Question 3.How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?Answer:

Question 4.How many real solutions does the quadratic equation x2 + 3x + 2 = 0 have? How do you know? What are the solutions?Answer:

**Solve the equation by graphing.**Question 1.

Question 55.**REASONING**Write a quadratic function in the form f = x2 + bx + c that has zeros 8 and 11.Answer:

Question 56.**NUMBER SENSE**Write a quadratic equation in standard form that has roots equidistant from 10 on the number line.Answer:

Question 61.**PROBLEM SOLVING**You make a rectangular quilt that is 5 feet by 4 feet. You use the remaining 10 square feet of fabric to add a border of uniform width to the quilt. What is the width of the border?Answer:

3i + Answer:

+ Answer:

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