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3.3 Quadratic Equations & Inequalities

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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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Presentation Transcript
slide2
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
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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