9-1 quadratic equations and functions 9-2 characteristics of quadratic functions 9-3 graphing...
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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
PreviewPreview
Warm Ups
Warm Up
1. Evaluate x2 + 5x for x = 4 and x = –3.
2. Generate ordered pairs for the function y = x2 + 2 for x-values
36; –6
–2, –1, 0, 1, and 2.
x –2 –1 0 1 2
y 6 3 2 3 6
9-1 Quadratic Equations and 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
9-2 Characteristics of Quadratic Functions
Warm UpFind 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
(–2, 1) (0, 2)
9-3 Graphing Quadratic Functions
Warm Up
1. Graph y = x2 + 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 UpFind 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
9-5 Solving Quadratic Equations by Factoring
Warm UpFind each square root.
Solve each equation.
5. –6x = –60 6.
7. 2x – 40 = 0 8. 5x = 3
6
11
–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
9-7 Completing 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
Warm Up
Evaluate for x = –2, y = 3, and z = –1.
6 1. x2 2. xyz
3. x2 – yz 4. y – xz
4
5. –x 6. z2 – xy
7 1
7 2
9-8 The Quadratic Formula
Warm UpUse the Quadratic Formula to solve each equation.
1. x2 – 5x – 6 = 0
2. 2x2 + 2x – 24 = 0
3. x2 + 10x + 25 = 0 0, –5
3, –4
1, –6
9-9 The Discriminant