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Polynomial Functions Exponents- Coefficients- Degree- Leading Coefficient-

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Constant Function- Linear Function- Quadratic Function- Ex) Write an equation for the linear function f such that f(3)=4 and f(-2)=-1.

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Quadratic Functions Ex) Graph (sketch) f(x)=(x–3) 2 +5 Vertex: Opens: Axis of Symmetry Equation of a Quadratic Function in Vertex Form f(x)=a(x-h) 2 +k Vertex:Axis of Symmetry: a:

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Ex) Find the vertex, axis of symmetry, and determine which direction the parabola opens. a) f(x)=-(x+2) 2 -4b) g(x)=3x 2 Equation of a Quadratic Function in Standard Form f(x)=ax 2 +bx+c

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Ex) Find the vertex and axis of symmetry of the parabola. f(x)=3x 2 +6x+7

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If asked to describe a quadratic function/graph, use the following words: Vertex, axis of symmetry, opens, stretch/shrink, even, x-intercept, y-intercept, etc. Ex) Write a quadratic function given a vertex (1, 5) and point (4, 8).

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Linear Correlation Strength Direction

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Examples of Linear Modeling Word Problems Constant rate of change (slope) Depreciation Examples of Quadratic Modeling Word Problems 2 things changing Area of rectangle, free fall motion, min/max value

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Ex) A car depreciated to $17,000 after 3 years. If the initial cost was $25,000, what was the value for the 6 th year? Write an equation to model this problem and find the answer. *If the question says that something depreciates and doesn’t give a value it depreciated to, that means it depreciated to $0.

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Projectile Motion/Free Fall Motion

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Ex) Jill threw a ball in the air from a height of 4 ft with initial velocity 20 ft/sec. a) Write the function. b) What’s the maximum height of the ball? c) How long does it take to get to the max. height? d) When is it at 9 ft? e) After how long does the ball hit the ground?

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Ex) T.F. South sells cans of pop in vending machines. They find that sales average 10,000 cans per month when the cans are $0.50 each. For each nickel increase in price, the sales per month drop by 500 cans. a) Determine a function R(x) for total revenue where x is the number of $0.05 increases in price. b) How much should TFS charge per can for maximum revenue?

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Graphing Quadratic Functions (2.1.1) October 1st, 2015.

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