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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. Solve quadratic equations by factoring Solve by square root method

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3.3 Quadratic Equations & Inequalities

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  1. 3.3 Quadratic Equations & Inequalities

  2. 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.

  3. Quadratic Equations • Solve quadratic equations by factoring • Solve by square root method • Solve by the quadratic formula.

  4. Quadratic Equation in one variable • Quadratic equation in standard form: ax2 +bx + c = 0 a ≠ 0

  5. 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.

  6. 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.

  7. 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

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

  9. Discriminant and Graph

  10. 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

  11. 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

  12. 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

  13. 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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