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β’ A quadratic equation in one variable is an equation that can be written in the standard form ππ₯ 2 + ππ₯ + π₯ = 0, where π, π, πππ π are real numbers and π β 0. β’ A root of an equation is a solution of the equation. WAYS TO SOLVE QUADRATIC EQUATIONS 1. SOLVING BY GRAPHING 2. SOLVING USING SQUARE ROOTS 3. SOLVING BY FACTORING (AKA ZERO-PRODUCT PROPERTY) WHEN SOLVING BY GRAPHING: 1. PUT THE EQUATION INTO STANDARD FORM: ππ₯ 2 + ππ₯ + π = 0 2 2. GRAPH THE RELATED FUNCTION: π¦ = ππ₯ + ππ₯ + π 3. THE SOLUTIONS TO THE EQUATION WILL BE THE X-INTERCEPTS (AKA ROOTS) SOLVE π₯ + 2π₯ = 3 BY GRAPHING 2 β’STEP 1: GET THE EQUATION INTO STANDARD FORM π₯ 2 + 2π₯ β 3 = 0 β’STEP 2: DETERMINE THE RELATED FUNCTION π¦ = π₯ 2 + 2π₯ β 3 β’STEP 3: FIND THE VERTEX β1, β4 β’STEP 4: MAKE A TABLE OF VALUES x y βπ βπ βπ β4 0 1 CONTINUED β’STEP 5: GRAPH β’STEP 6: WRITE THE SOLUTIONS π₯ = β3 AND π₯ = 1 SOLVE π₯ + 8 = 6π₯ BY GRAPHING 2 Standard Form: Related Function: x y Solutions: SOLVE π₯ = β7π₯ β 10 BY GRAPHING 2 Standard Form: Related Function: x y Solutions: SOLVE π₯ β 8π₯ = β16 BY GRAPHING 2 Standard Form: Related Function: x y Solutions: SOLVE βπ₯ = 2π₯ + 4 BY GRAPHING 2 Standard Form: Related Function: x y Solutions: HOMEWORK β’10.3 HOMEWORK WORKSHEET (ALL PROBLEMS)