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Using The Quadratic Formula 34 Exercises

Vocabulary and Core Concept CheckQuestion 1.COMPLETE THE SENTENCEWhen 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 SENTENCEYou 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

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Quadratic Equations And Complex Numbers Mathematical Practices

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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:


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Lesson 34 Using The Quadratic Formula

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


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


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

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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.


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:

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

Download the Topic-wise BigIdeas math book textbook solutions of algebra 2 ch 3 Quadratic Equations and Complex Numbers pdf for free of charge and practice well at any time and anywhere you wish. Once you start preparing the concepts of chapter 3 from BIM Textbook Solution Key, you can stand out from the crowd and become a topper in the class. Just tap on the available links below and freely. These solutions of BIM Algebra 2 Quadratic Equations and Complex Numbers are prepared by the subject experts according to the guidelines of the Common core standards.

Question 15.ABSTRACT REASONINGDetermine 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

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


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


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.REASONINGA 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:


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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?


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


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

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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.REASONINGWrite a quadratic function in the form f = x2 + bx + c that has zeros 8 and 11.Answer:

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

Question 61.PROBLEM SOLVINGYou 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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