Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

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Presentation transcript:

Chapter 4: Polynomial and Rational Functions

4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is In this formula, is called the Discriminant, which tells the nature of the roots of a quadratic equations (real, imaginary, double).

If the discriminant is: Discriminant A negative number, then you will have… Zero, then you will have… A positive number, then you will have… 4-2 Quadratic Equations

Example 1: Find the discriminant of the equation and describe the nature of the roots of the equation. Solve the equation by using the Quadratic Formula 3x 2 – 4x + 7 = Quadratic Equations

Problem 1: Find the discriminant of the equation and describe the nature of the roots of the equation. Solve the equation by using the Quadratic Formula x 2 – 6x – 12 = Quadratic Equations

Example 2: Solve 2x 2 +6x + 5 = 0 by completing the square. 4-2 Quadratic Equations

Problem 2: Solve x 2 – 6x – 7 = 0 by completing the square. 4-2 Quadratic Equations

Problem 3: Solve: quadratic formula, complete square, factoring, or graphing. x 2 – 36 = Quadratic Equations

x 2 + 6x + 5 = Quadratic Equations Problem 4: Solve: quadratic formula, complete square, factoring, or graphing.

HW 4-2 pg. 219 #13-33 odd 4-2 Quadratic Equations