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MAT 150 – Algebra Class #8

MAT 150 – Algebra Class #8. Topics: Standard and Vertex form of a Quadratic Function Finding Key Features of a Quadratic algebraically and graphically. Graphing Quadratics. Several key features can be determined from the standard form: Concavity Vertex (minimum or maximum)

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MAT 150 – Algebra Class #8

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  1. MAT 150 – AlgebraClass #8 Topics: Standard and Vertex form of a Quadratic Function Finding Key Features of a Quadratic algebraically and graphically. Graphing Quadratics

  2. Several key features can be determined from the standard form: • Concavity • Vertex (minimum or maximum) • Axis of Symmetry • y-intercepts • X-intercepts • ALL QUADRATICS ARE A PARABOLA! Standard Form of a Quadratic Equation

  3. If a > 0, the parabola is concave up. If a < 0, the parabola is concave down. Determining Concavity

  4. Finding the Vertex (min/max)

  5. Vertex Form of a Quadratic

  6. Suppose the monthly revenue from the sale of Carlson 42-inch 3D televisions is given by the function dollars, where x is the number of televisions sold. • How many televisions must be sold to make a maximum amount of revenue? • What is the maximum amount of revenue to be made? • For how many televisions would the monthly revenue be increasing? Using the Vertex in a Real-Life Situation

  7. Steps • Find the vertex • Make a table of values centered around the vertex. (At least 5 points) • Graph on a coordinate plane. Graph the following: Graphing Quadratic Functions

  8. Finding x- and y-intercepts graphically

  9. A ball is thrown upward at 64 ft per second from the top of an 80-foot-high building given by the function . • How high does the ball go? • How long did it take to reach the maximum height? • When will the ball hit the ground? • How high is the ball when it is first thrown? • How long will it take the ball to reach a height of 130ft? Putting it all together

  10. Pg. 178-182 #1-4 all #21-24 all #57-63 all Assignment

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