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WARM UP WHAT TO EXPECT FOR THE REST OF THE YEAR 4 May 28 9.7 The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June 3 10.1 Adding Polynomials June 4 10.1 Subtracting Polynomials June 5 10.2 Multiplying Polynomials June 6 10.2 Multiplying Polynomials June 7 Special Products of Polynomials June 10 Special Products of Polynomials June 11 Chapter 10 Test Review June 12 Chapter 10 Test June 13 Finals Review June 14 Finals Review June 17 Finals June 18 Finals

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WHAT TO EXPECT FOR THE REST OF THE YEAR WARM UP 3 May 28 9.7 The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June 3 10.1 Adding Polynomials June 4 10.1 Subtracting Polynomials June 5 10.2 Multiplying Polynomials June 6 10.2 Multiplying Polynomials June 7 Special Products of Polynomials June 10 Special Products of Polynomials June 11 Chapter 10 Test Review June 12 Chapter 10 Test June 13 Finals Review June 14 Finals Review June 17 Finals June 18 Finals

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WHAT TO EXPECT FOR THE REST OF THE YEAR WARM UP 2 May 28 9.7 The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June 3 10.1 Adding Polynomials June 4 10.1 Subtracting Polynomials June 5 10.2 Multiplying Polynomials June 6 10.2 Multiplying Polynomials June 7 Special Products of Polynomials June 10 Special Products of Polynomials June 11 Chapter 10 Test Review June 12 Chapter 10 Test June 13 Finals Review June 14 Finals Review June 17 Finals June 18 Finals

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WHAT TO EXPECT FOR THE REST OF THE YEAR WARM UP 1 May 28 9.7 The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June 3 10.1 Adding Polynomials June 4 10.1 Subtracting Polynomials June 5 10.2 Multiplying Polynomials June 6 10.2 Multiplying Polynomials June 7 Special Products of Polynomials June 10 Special Products of Polynomials June 11 Chapter 10 Test Review June 12 Chapter 10 Test June 13 Finals Review June 14 Finals Review June 17 Finals June 18 Finals

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WHAT TO EXPECT FOR THE REST OF THE YEAR WARM UP 0 May 28 9.7 The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June 3 10.1 Adding Polynomials June 4 10.1 Subtracting Polynomials June 5 10.2 Multiplying Polynomials June 6 10.2 Multiplying Polynomials June 7 Special Products of Polynomials June 10 Special Products of Polynomials June 11 Chapter 10 Test Review June 12 Chapter 10 Test June 13 Finals Review June 14 Finals Review June 17 Finals June 18 Finals

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GOAL Use the discriminant to determine the number of solutions of a quadratic equation. KEY WORDS Discriminant 9.7 Using the Discriminant

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THE NUMBER OF SOLUTIONS OF A QUADRATIC EQUATION 9.7 Using the Discriminant Consider the quadratic equation ax 2 + bx + c = 0 If the value of b 2 – 4ac is positive, then the equation has two solutions. If the value of b 2 – 4ac is zero, then the equation has one solution. If the value of b 2 – 4ac is negative, then the equation has no real solution.

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EXAMPLE 1 EXAMPLE 1 Find the Number of Solutions Find the value of the discriminant. Then use the value to determine whether x 2 - 3x - 4 = 0 has two solutions, one solution, or no real solutions. SOLUTION x 2 - 3x - 4 = 0 Identify a =1, b = -3 and c = -4 b 2 – 4ac = (-3) 2 – 4(1)(-4) Substitute values for a, b, and c. = 9 + 16 Simplify = 25 Discriminant is positive. ANSWER> The discriminant is positive, so the equation has two solutions. 9.7 Using the Discriminant

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Because each solution of ax 2 + bx + c = 0 represents an x-intercept of y = ax 2 + bx + c, you can use the discriminant to determine the number of times the graph of a quadratic function intersects the x-axis. These points are called the x-intercepts or roots. 9.7 Using the Discriminant y = x 2 – x - 2 (-1, 0)(2, 0) x-intercept

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EXAMPLE 2 EXAMPLE 2 Find the x-intercepts Determine whether the graph of y = x 2 + 2x – 2 will intersect the x-axis in zero, one, or two points. SOLUTION Let y = 0. Then find the value of the discriminant x 2 + 2x – 2 = 0. x 2 + 2x – 2 = 0 Identify a =1, b = 2 and c = -2 b 2 – 4ac = (2) 2 – 4(1)(-2) Substitute values for a, b, and c. = 4 + 8 Simplify = 12 Discriminant is positive. ANSWER> The discriminant is positive, so the equation has two solutions and the graph will intersect the x-axis in two points. 9.7 Using the Discriminant

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Checkpoint Find the Number of Solutions. Find the value of the discriminant. Then use the value to determine whether the equation has two solutions, one solution, or no real solution. 1.x 2 – 3x + 4 = 0 2.x 2 - 4x + 4 = 0 3.x 2 - 5x + 4 = 0 9.6 Solving Quadratic Equations by the Quadratic Formula

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