SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The.

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Presentation transcript:

SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The Quadratic Formula and the Discriminant

How to Solve a Quadratic Equations 1) Graph to find x-intercepts(5.2) Difficult to do without a graphing calculator. Answers are real numbers only. 2) Factoring(5.3) Only works if the trinomial/binomial is factorable. Answers are real numbers only. 3) Square root(5.4) Only works for x² equations without a middle term. Answers can be real or imaginary numbers. 4) Quadratic Formula(5.6) Can be used for any equation in the form ax² + bx + c = 0. Answers can be real or imaginary numbers.

Quadratic Formula

Solve using the Quadratic Formula 1) x² + 6x = 162) x² - 6x + 2 = 0

3) x² - 16x + 64 = 04) x² + 13 = 6x

Discriminant  The expression under the square root b² - 4ac.  Used to determine the number and type of roots of a quadratic equation. b² - 4ac > 02 real roots b² - 4ac = 01 real root b² - 4ac < 02 complex roots

a)Find the value of the discriminant b)Describe the number and type of roots. c) Find the exact solutions by using the quadratic formula. 1) x² - 11x + 10 = 02) x² + 3x + 5 = 0 3) 2x² - 4x + 1 = 04) x² + 3x + 8 = 5