Analyzing Graphs of Quadratic Functions

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Section 2.4

• Analyzing Graphs of Quadratic Functions

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Quadratic Equation

• Quadratic Equation
• y ax2 bx c 0
• where a, b, c are constants and a 0
• Second-degree equations
• Graph of quadratic is
• known as a parabola
• Graph is not a straight line, but the shape of a
  curve

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Parabola

• Parabolas are symmetric.
• Axis of Symmetry-The line through the vertex
  about which the parabola is symmetric.

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Minimum or maximum values of a function occur at
the VERTEX.

• P(x) a(x h)2 k
• Vertex of parabola (h, k)
• a gt 0 parabola opens up (h,k) minimum point
• Minimum Value of function is P(h)k
• a lt 0 parabola opens down (h,k)maximum point
• Maximum Value of function is P(h)k
• Minimum/Maximum values are based on y-values

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Vertex Formula

• P(x) ax2 bx c (a ? 0)
• The following formula will give you the
  x-value for the vertex of a quadratic
• X
• Coordinates of vertex

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To Graph a Quadratic Function

• Find the coordinates of the vertex.
• (Use the vertex formula.)
• Determine which way parabola opens by looking at
  a.
• a gt 0 parabola opens up (Vertex is lowest point)
• a lt 0 parabola opens down (Vertex is highest
  point)
• Find the x-intercept(s). (Set y 0)
• Find the y-intercept. (Set x 0)
• Graph additional points if needed by t-chart or
  symmetry.

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