 ## Presentation on theme: "9-1 Quadratic Equations and Functions 9-2 Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions 9-4 Solving Quadratic Equations by Graphing."— Presentation transcript:

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 DiscriminantPreview Warm Ups

Warm Up 1. Evaluate x 2 + 5x for x = 4 and x = –3. 2. Generate ordered pairs for the function y = x 2 + 2 for x-values 36; – 6 – 2, – 1, 0, 1, and 2. x –2–2 –1–1 012 y 6 3236 9-1 Quadratic Equations and Functions

Warm Up Find the x-intercept of each linear function. 1. y = 2x – 32. 3. y = 3x + 6 Evaluate each quadratic function for the given input values. 4. y = –3x 2 + x – 2, when x = 2 5. y = x 2 + 2x + 3, when x = –1 –2 –12 2 9-2 Characteristics of Quadratic Functions

Warm Up Find the axis of symmetry. 1. y = 4x 2 – 72. y = x 2 – 3x + 1 3. y = –2x 2 + 4x + 34. y = –2x 2 + 3x – 1 Find the vertex. 5. y = x 2 + 4x + 56. y = 3x 2 + 2 7. y = 2x 2 + 2x – 8 x = 0 x = 1 (–2, 1) (0, 2) 9-3 Graphing Quadratic Functions

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

Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial. 4. x 2 + 12x + 355. x 2 + 2x – 63 6. x 2 – 10x + 167. 2x 2 – 16x + 32 x 2 + 9x + 14 x 2 – 6x – 55 x 2 – 20x + 100 (x + 5)(x + 7)(x – 7)(x + 9) (x – 2)(x – 8)2(x – 4) 2 9-5 Solving Quadratic Equations by Factoring

Warm Up Find each square root. Solve each equation. 5. –6x = –606. 7. 2x – 40 = 08. 5x = 3 611 –25 1. 2. 3. 4. x = 10 x = 80 x = 20 9-6 Solving Quadratic Equations by Using Square Roots

Warm Up Part I Simplify. 19 1.2. 3.4. 9-7 Completing the Square

Warm Up Part II Solve each quadratic equation by factoring. 5. x 2 + 8x + 16 = 0 6. x 2 – 22x + 121 = 0 7. x 2 – 12x + 36 = 0 –4 11 6

Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x6. z 2 – xy 71 7 2 9-8 The Quadratic Formula

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