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2.3 Quadratic Functions

2.3 Quadratic Functions. A quadratic function is a function of the form:. Properties of the Graph of a Quadratic Function. Parabola opens up if a > 0 ; the vertex is a minimum point. Parabola opens down if a < 0 ; the vertex is a maximum point.

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2.3 Quadratic Functions

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  1. 2.3Quadratic Functions

  2. A quadratic function is a function of the form:

  3. Properties of the Graph of a Quadratic Function Parabola opens up if a > 0; the vertex is a minimum point. Parabola opens down if a < 0; the vertex is a maximum point.

  4. Graphs of a quadratic function f(x) = ax2 + bx + c Vertex is highest point Axis of symmetry Axis of symmetry a> 0 a< 0 Opens up Opens down Vertex is lowest point

  5. Steps for Graphing a Quadratic Function by Hand • Determine the vertex. • Determine the axis of symmetry. • Determine the y-intercept, f(0). • Determine how many x-intercepts the graph has. • If there are no x-intercepts determine another point from the y-intercept using the axis of symmetry. • Graph.

  6. Without graphing, locate the vertex and find the axis of symmetry of the following parabola. Does it open up or down? Vertex: Since -3 < 0 the parabola opens down.

  7. Finding the vertex by completing the square:

  8. (2,4) (0,0)

  9. (0,0) (2, -12)

  10. (2, 0) (4, -12)

  11. Vertex (2, 13)

  12. Determine whether the graph opens up or down. Find its vertex, axis of symmetry, y-intercept, x-intercept. x-coordinate of vertex: y-coordinate of vertex: Axis of symmetry:

  13. There are two x-intercepts:

  14. (0, 5) (-5.55, 0) (-0.45, 0) Vertex: (-3, -13)

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