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Transcript
Section 1.2 Quadratic Equations Objectives: Solve quadratic equations by factoring, square root method, and the quadratic formula. Review of Factoring Factoring polynomials – rewriting as a product. With all types of factoring, always check for a greatest common factor (GCF) first. The GCF can be a monomial, a binomial, or used to factor by grouping. Polynomials that cannot be factored are said to be prime. Special Formulas Difference of Two Squares: A 2 B 2 A B A B Difference of Two Cubes: A 3 B 3 A B A 2 AB B 2 Sum of Two Cubes: A 3 B 3 A B A 2 AB B 2 1.2 - 2 Factoring Trinomials Trinomials of the Form x 2 Bx C : Look for two numbers whose product is C and whose sum is B. Trinomials of the form Ax 2 Bx C : 1. Look for two numbers whose product is A C and whose sum is B. 2. Rewrite the middle term as the sum of the two factors. 3. Factor by grouping. Perfect Square Trinomials: A 2 2 AB B 2 A B 2 A 2 2 AB B 2 A B 2 Work #1 - 6 Quadratic Equations A quadratic equation is one that can be written in the form ax 2 bx c 0 . Also called second-degree equations. Zero-Product Property – set each factor equal to 0, then solve the resulting equations. 1.2 - 3 Solve Quadratic Equations by Factoring: 1. Write in standard form, if necessary. 2. Factor 3. Use zero-product property. Work #7 - 10 Solve Quadratic Equations Using the Square Root Property: To solve equations of the form ax 2 c 0 , isolate the squared term on one side, then take the square root of both sides. Don’t forget, you need the positive and the negative roots. Work #11 – 12 Solve Quadratic Equations Using the Quadratic Formula: If you solve the standard form of a quadratic equation, ax 2 bx c 0 , by completing the square, the result is the Quadratic Formula. b b 2 4ac x 2a Work #13 - 19