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5.2 Properties of Parabolas

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y = ax 2 + bx + c Standard Form c is the y-intercept. If b = 0 then y = ax 2 + c Axis of symmetry: x = 0 Vertex (0, c)

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EX 1 Graph: y =

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If a > 0 then opens up. If a < 0 then opens down. Axis of Symmetry: x =

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EX 2 Graph y =

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The y value of the vertex is the maximum or minimum of the quadratic function.

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EX 3 Graph y =

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EX 4 Find two numbers with a difference of 10 and a product that is a minimum. Find the minimum product.

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EX 5 Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?

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