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ca_m4

# ca_m4 - MAC 1105 Module 4 Quadratic Functions and Equations...

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Rev.S08 MAC 1105 Module 4 Quadratic Functions and Equations

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Rev.S08 2 Learning Objectives Upon completing this module, you should be able to: 1. Understand basic concepts about quadratic functions and their graphs. 2. Complete the square and apply the vertex formula. 3. Graph a quadratic function by hand. 4. Solve applications and model data. 5. Understand basic concepts about quadratic equations. 6. Use factoring, the square root property, completing the square, and the quadratic formula to solve quadratic equations. Understand the discriminant. Solve problems involving quadratic equations. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.

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Rev.S08 4 What is a Quadratic Function? Recall that a linear function can be written as f ( x ) = ax + b (or f ( x ) = mx + b ). The formula for a quadratic function is different from that of a linear function because it contains an x 2 term. f ( x ) = 3 x 2 + 3 x + 5 g ( x ) = 5 - x 2 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Rev.S08 5 Quadratic Functions (Cont.) The graph of a quadratic function is a parabola —a U shaped graph that opens either upward or downward . A parabola opens upward if a is positive and opens downward if a is negative. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.

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Rev.S08 6 Quadratic Functions (Cont.) The highest point on a parabola that opens downward and the lowest point on a parabola that opens upward is called the vertex . The vertical line passing through the vertex is called the axis of symmetry . The leading coefficient a controls the width of the parabola . Larger values of | a | result in a narrower parabola, and smaller values of | a | result in a wider parabola. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Rev.S08 7 Example of Different Parabolas http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Note: A parabola opens upward if a is positive and opens downward if a is negative.

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