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f(x) = x2 Let’s review the basic graph of f(x) = x2 x f(x) = x2 -3 9
-2 4 -1 1 2 3 10 9 8 7 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -5 -6

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Standard Form The graphs of quadratic functions are parabolas
If a > 0, the parabola opens upward If a < 0, the parabola opens downward Vertex => (h,k) Axis of symmetry => x = h h controls vertex movement left and right k controls vertex movement up and down vertex axis of symmetry Examples: Find the coordinates of the vertex for the given quadratic functions and give the axis of symmetry Vertex: Axis of symmetry: Opens ____________ Vertex: Axis of symmetry: Opens ____________ Vertex: Axis of symmetry: Opens ____________

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Examples Graph the quadratic function. Give the axis of symmetry, domain, and range of each function. 6 6 5 5 4 4 3 3 2 2 1 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 See pg 288 in the book for a 5-step guide to graphing quadratic functions in standard form

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Another Form Another common form is used for parabolas as well
vertex Functions of this form can be converted to standard form by completing the square If a > 0, the parabola opens upward If a < 0, the parabola opens downward Vertex => Find x-intercepts by solving f(x) = 0 Find y-intercept by finding f(0) axis of symmetry Examples: Find the coordinates of the vertex for the given quadratic functions and give the x and y intercepts Vertex: x-intercepts: y-intercept: Vertex: x-intercepts: y-intercept: Vertex: x-intercepts: y-intercept:

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Examples Book problems: 9,13,15,17,21,23,27,30,33,37 Graph the quadratic function. Give the axis of symmetry, domain, and range of each function. 6 6 5 5 4 4 3 3 2 2 1 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 See pg 292 in the book for a 5-step guide to graphing quadratic functions in standard form and applications

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