3 3 quadratic equations inequalities
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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

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3 3 quadratic equations inequalities

3.3 Quadratic Equations & Inequalities


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

Quadratic Equations

  • Solve quadratic equations by factoring

  • Solve by square root method

  • Solve by the quadratic formula.


Quadratic equation in one variable

Quadratic Equation in one variable

  • Quadratic equation in standard form:

ax2 +bx + c = 0 a ≠ 0


Solve by factoring

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

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.


Quadratic formula

Quadratic formula

  • 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

Discriminant

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


Discriminant and graph

Discriminant and Graph


Solving quadratic inequalities

Solving Quadratic Inequalities

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


Solving quadratic inequalities1

Solving Quadratic Inequalities

  • 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


Solving quadratic inequalities2

Solving Quadratic Inequalities

  • 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

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

  • Reading: 3.4 Modeling

  • Reminder: Project 2 Due March 2nd

    Skill test 2 Due March 4th

    Exam 2 March 7th,8th


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