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# 3.3 Quadratic Equations & Inequalities - PowerPoint PPT Presentation

3.3 Quadratic Equations &amp; 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 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

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