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Mastering Graphing Quadratic Functions: A Comprehensive Guide

Learn how to graph quadratic functions with this detailed guide covering vertex form, standard form, and intercept form methods. Understand concepts like axis of symmetry, vertex coordinates, and how to convert equations between different forms easily.

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Mastering Graphing Quadratic Functions: A Comprehensive Guide

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  1. Warm Up

  2. Graphing Quadratic Functions

  3. Graphing Quadratic Functions Brainstorm everything you know about a quadratic function.

  4. THE GRAPH OF A QUADRATIC FUNCTION The parabola opens up if a>0 and opens down if a<0 y = x2 The parabola is wider than the graph of y = x2 if |a| < 1 and narrower than the graph of y = x2 if |a| > 1. vertex y = -x2 Axis of symmetry

  5. STANDARD FORM Graph y = 2x2 -8x +6 Solution: The coefficients for this function Since a>0, the parabola opens up. The x-coordinate is: x = -b/2a The y-coordinate is: The vertex is a = 2, b = -8, c = 6. x = -(-8)/2(2) x = 2 y = 2(2)2-8(2)+6 y = -2 (2,-2).

  6. GRAPH VERTEX: AXIS OF SYMMETRY: Y INTERCEPT:

  7. VERTEX FORM OF QUADRATIC EQUATION y = a(x - h)2 + k • The vertex is (h,k). • The axis of symmetry is x = h.

  8. GRAPHING A QUADRATIC FUNCTION IN VERTEX FORM Example y = -1/2(x + 3)2 + 4 VERTEX: AXIS OF SYMMETRY: Y INTERCEPT:

  9. INTERCEPT FORM OF QUADRATIC EQUATION y = a(x - p)(x - q) • The x intercepts are p and q. • The axis of symmetry is halfway between (p,0) and (q,0).

  10. GRAPHING A QUADRATIC FUNCTION IN INTERCEPT FORM Example y = -(x + 2)(x - 4). VERTEX: AXIS OF SYMMETRY: Y INTERCEPT: X INTERCEPT:

  11. WRITING THE QUADRATIC EQUATION IN STANDARD FORM (1). y = -(x + 4)(x - 9) (2). y = 3(x -1)2 + 8 -x2 + 5x + 36 3x2 - 6x + 11

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