5.2 Properties of Parabolas

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5.2 Properties of Parabolas
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y ax2 bx cStandard Form

• c is the y-intercept.
• If b 0 then y ax2 c
• Axis of symmetry x 0
• Vertex (0, c)

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EX 1

• Graph y

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• If a gt 0 then opens up.
• If a lt 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?