# 3.3 Quadratic Equations & Inequalities - PowerPoint PPT Presentation

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3.3 Quadratic Equations & Inequalities. Quiz. Tell true or false of the following statement: given linear functions f(x) and g(x), if ( fg )(x) = 0, then either f(x) = 0 or g(x) = 0. Quadratic Equations. Solve quadratic equations by factoring Solve by square root method

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## 3.3 Quadratic Equations & Inequalities

### Quiz

• Tell true or false of the following statement:

given linear functions f(x) and g(x), if (fg)(x) = 0, then either f(x) = 0 or g(x) = 0.

• Solve quadratic equations by factoring

• Solve by square root method

• Solve by the quadratic formula.

### Quadratic Equation in one variable

• Quadratic equation in standard form:

ax2 +bx + c = 0 a ≠ 0

### Solve by Factoring

• 3y(y - 1) = 0

• X2 – 49 = 0

• X2 + 11x = 12

• 6p2 – 5p = 6

• 2x2 + 4x -16 = 0

• X2 -6x + 9 =0

Fact:

Given two functions f(x) and g(x), if (fg)(x) = 0, then either f(x) = 0 or g(x) = 0.

### Square root method

• x2 = 49

• (4x - 3)2 = 36

• (1 - z)2 = 8

• (a + 2)2 = -5

Fact:

Given a function f(x) , if ( f(x) )2 = B, B ≥ 0, then f(x) = ± √ B.

• x2 + 5x + 7 = 0

• 3p2 + 7p -2 = 0

• (x - 3)(x + 5) = -7

The solutions of the quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by the formula

x =

- b ± √ b2 – 4ac

2a

### Discriminant

• b2 – 4ac is called the discriminant of the quadratic equation

### Discriminant and Graph

x1

x2

x

x1

x2

x

If x1 < x < x2, then f(x) < 0

If x = x1 or x2, then f(x) = 0

If x < x1 or x > x2, then f(x)> 0

If x1 < x < x2, then f(x) > 0

If x = x1 or x2, then f(x) = 0

If x < x1 or x > x2, then f(x)< 0

• 1. Solve the corresponding quadratic equation

Finding the x- intercepts of the function

• 2. Identify the intervals determined by the solutions of the equation

• 3. Use a test value from each interval to determine which intervals from the solution set

• x2 + 4x -12 ≥ 0

• x(x-7) < 8

• x2 + 4x +4 < 0

• x2 + 6x +9 > 0

• 2x2+ 4x +4 < 0

• -x2 + 4x - 6 > 0

### Homework

• PG. 189: 5 – 50(M5),51,55,60

• PG. 190: 63,66,68, 72 – 93(M3), 95 – 103(odds)

• KEY: 30, 45, 51, 95