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f(x) = x 2

f(x) = x 2. Let’s review the basic graph of f(x) = x 2. 10. 9. 8. 7. 6. 5. 4. 3. 2. 1. -6. -5. -4. -3. -2. -1. 1. 2. 3. 4. 5. 6. -5. -6. Standard Form. The graphs of quadratic functions are parabolas Standard form. If a > 0, the parabola opens upward

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f(x) = x 2

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

  2. Standard Form • The graphs of quadratic functions are parabolas • Standard form • 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 ____________

  3. 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

  4. 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:

  5. 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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