This document discusses key concepts about quadratic functions including that they form parabolas with an axis of symmetry, how to identify the a, b, and c coefficients, and that the vertex represents the minimum or maximum value depending on whether a is positive or negative. It also explains how to graph quadratic functions using a table of values on a calculator or by hand and how the width of the parabola relates to the value of a.

1. Exploring Quadratic Functions

2. Quadratic Functions Quadratic Functions Form parabolas The line down the center of a parabola is called the axis of symmetry

3. Example 1a: Standard Form ax 2 + bx + c = y a ≠ 0 Why can’t the value of a be = to 0? You will be asked to identify the a, b & c coefficients in a quadratic function.

4. Vertex If a > 0, the parabola opens upwards And has a minimum If a < 0, the parabola opens downwards And has a maximum The minimum or maximum is called the vertex. You will be asked to tell whether a function is opening upwards or downwards and has a minimum or maxium.

5. Graphing using a table of values You can graph a quadratic function using a table of values. This table of values can be created on paper or using your graphing calculator. Look at the table of values on page 319 of your textbook.

6. Example 1b Now put y=2x 2 into your calculator and you’ll see the same table. Use this table to graph the equation on your paper. Add y=-2x 2 to the function editor. Use table of values -3 to 3 when possible. You can do more than one equation on the function editor/table at a time.

7. Example 2: Ordering Quadratic Functions based on width Graph y = -4x 2 ; y = ¼ x 2 ; y = x 2 Which is the widest? Which is the narrowest? How does this compare with what you know about slope? You will be asked to order basic quadratic functions from widest to narrowest. Remember that widest and narrowest will be relative depending on the coefficient.