Chapter 3 Review and Tests

Review

Definitions, Concepts, and Formulas Examples

3.1 Quadratic Functions

  1. A quadratic function f is a function of the form

    f(x)=ax2+bx+c, a0.
  2. The standard form of a quadratic function is

    f(x)=a(x  h)2+k, a0.
  3. The graph of a quadratic function is a transformation of the graph of y=x2.

  4. The graph of a quadratic function is a parabola with vertex

    (h,k)=(b2a,f(b2a)).
  5. The maximum (if a<0) or minimum (if a>0) value of a quadratic function f(x)=ax2+bx+c is the y-coordinate, k, of the vertex of the parabola.

  1. Sketch the graph of f(x)=2x2+4x+6.

    Solution

    We can put f into standard form:

    f(x)=2x2+4x+6=2(x1)2+8.

    The graph of f is the graph of y=x2 shifted 1 unit to the right, stretched vertically by a factor ...

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