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Section 2.4 Analyzing Graphs of Quadratic Functions

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Quadratic Equation Quadratic Equation: y = ax 2 + 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 > 0 parabola opens up (h,k) = minimum point Minimum Value of function is P(h)=k a < 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) = ax 2 + 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 1.Find the coordinates of the vertex. (Use the vertex formula.) 2.Determine which way parabola opens by looking at a. a > 0 parabola opens up (Vertex is lowest point) a < 0 parabola opens down (Vertex is highest point) 3.Find the x-intercept(s). (Set y = 0) 4.Find the y-intercept. (Set x = 0) 2.Graph additional points if needed by t-chart or symmetry.

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