Module 11 topic 1

Module 11 Topic 1 Graphing and Solving Quadratic Equations Goal 4: The learner will use relations and functions to solve problems and justify results. Objective 4.02: Graph, factor, and evaluate quadratic functions to solve problems.

Graphs of Quadratic Equations are called Parabolas Vertex Axis of Symmetry

y = ax 2 + bx + c ,[object Object],[object Object],a is a coefficient that determines if the parabola opens upward or downward a , b and c are used to find the vertex using the following formula Example 1: Determine if the parabola for the following functions open upward or downward. a) y = x 2 + 4x - 6 The graph opens upward because the value of a is 1 which is positive. b) y = -3x 2 + 6x – 2 The graph opens downward because the value of a is -3 which is negative.

Example 2: Find the Vertex ,[object Object],[object Object],y = x 2 – 6x + 4 a = 1 b = -6 c = 4

Example 3: Find the Vertex when b = 0 ,[object Object],[object Object],y = -3x 2 + 6 a = -3 b = 0 c = 6

Solving Quadratic Equations can be done by factoring or graphing. ,[object Object],y = x 2 + 5x + 6 a = 1 b = 5 c = 6 We need to find two factors that have a product of 6 and a sum of 5 . So 2 and 3 will work for this problem. Click on the parabolas to watch a short clip about solving quadratics. y = (x + 2)(x + 3) x + 2 = 0 x + 2 – 2 = 0 – 2 x = -2 x + 3 = 0 x + 3 – 3 = 0 - 3 x = -3 The quadratic equation crosses the x-axis at -2 and -3. These are called the roots, zeros, or solutions.

Module 11 topic 1

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