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9-1 Quadratic Equations and Functions 9-2 Characteristics of Quadratic Functions

Warm Ups. Preview. 9-1 Quadratic Equations and Functions 9-2 Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions 9-4 Solving Quadratic Equations by Graphing 9-5 Solving Quadratic Equations by Factoring 9-6 Solving Quadratic Equations by Using Square Roots

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9-1 Quadratic Equations and Functions 9-2 Characteristics of Quadratic Functions

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  1. Warm Ups Preview 9-1 Quadratic Equations and Functions 9-2 Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions 9-4 Solving Quadratic Equations by Graphing 9-5 Solving Quadratic Equations by Factoring 9-6 Solving Quadratic Equations by Using Square Roots 9-7 Completing the Square 9-8 The Quadratic Formula 9-9 The Discriminant

  2. x –2 –1 0 1 2 y 6 3 2 3 6 9-1 Quadratic Equations and Functions • Warm Up • 1. Evaluate x2 + 5x for x = 4 and x = –3. 36; –6 2. Generate ordered pairs for the function y = x2 + 2 for x-values –2, –1, 0, 1, and 2.

  3. 9-2Characteristics of Quadratic Functions Warm Up Find the x-intercept of each linear function. 1. y = 2x – 3 2. 3. y = 3x + 6 Evaluate each quadratic function for the given input values. 4. y = –3x2 + x – 2, when x = 2 5. y = x2 + 2x + 3, when x = –1 –2 –12 2

  4. 9-3Graphing Quadratic Functions Warm Up Find the axis of symmetry. 1. y = 4x2 – 7 2. y =x2 – 3x + 1 3. y = –2x2 +4x + 3 4.y = –2x2 + 3x – 1 Find the vertex. 5. y = x2 + 4x + 5 6. y = 3x2 + 2 7. y = 2x2 +2x – 8 x = 0 x = 1 (0, 2) (–2, 1)

  5. 9-4Solving Quadratic Equations by Graphing Warm Up 1. Graph y = x2 + 4x + 3. 2. Identify the vertex and zeros of the function above. vertex:(–2 , –1); zeros:–3, –1

  6. 9-5Solving Quadratic Equations by Factoring • Warm Up • Find each product. • 1. (x + 2)(x + 7) 2. (x – 11)(x + 5) • 3. (x – 10)2 • Factor each polynomial. • 4. x2 + 12x + 35 5. x2 + 2x – 63 • 6. x2 – 10x + 16 7. 2x2 – 16x + 32 x2 + 9x + 14 x2 – 6x – 55 x2 – 20x + 100 (x + 5)(x + 7) (x– 7)(x + 9) (x – 2)(x – 8) 2(x – 4)2

  7. 9-6Solving Quadratic Equations by Using Square Roots Warm Up Find each square root. Solve each equation. 5. –6x = –60 6. 7. 2x – 40 = 0 8. 5x = 3 1. 6 11 2. 4. –25 3. x= 80 x = 10 x = 20

  8. 9-7Completing the Square Warm Up Part I Simplify. 19 1. 2. 3. 4.

  9. 9-7Completing the Square • Warm Up Part II • Solve each quadratic equation by factoring. • 5. x2 + 8x + 16 = 0 • 6. x2– 22x + 121 = 0 • 7. x2 – 12x + 36 = 0 –4 11 6

  10. 9-8The Quadratic Formula Warm Up Evaluate for x = –2, y = 3, and z = –1. 1. x2 4 2. xyz 6 3. x2 – yz 4. y – xz 7 1 5. –x 6. z2 – xy 7 2

  11. 9-9The Discriminant • Warm Up • Use the Quadratic Formula to solve each equation. • 1. x2 – 5x – 6 = 0 • 2. 2x2 + 2x – 24 = 0 • 3. x2 + 10x + 25 = 0 1, –6 3, –4 0, –5

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