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5-1 Modeling Data With Quadratic Functions Big Idea: -Graph quadratic functions and determine maxima, minima, and zeros of function. -Demonstrate and explain the effect that changing a coefficient has on the quadratic function graph.

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Quadratic Function Standard Form f(x)= ax² + bx + c (a, b & c are numbers and a = 0) Quadratic term Linear term Constant term

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Ex 1: Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. A) y=(2x+3)(x - 4) B) f(x) = 3(x² -2x)-3(x² -2) C) g(x)= 8(x+9)

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Graphs of Parabolas +a The y-value of the vertex is the minimum point -a The y-value of the vertex is the maximum point

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Axis of symmetry: a line that divides a parabola into two parts that are mirror images.

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Ex 2:

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Ex 3: Find the quadratic function that includes each set of values. A) xy 23 313 429

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Essential Question: Describe the shape of the graph of a quadratic function. (how does the a, b, and c effect the graph)

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