6-1 Graphing Quadratic Functions Objectives Students will be able to: Graph quadratic functions Find and interpret the maximum and minimum values of a quadratic function

A quadratic function is a function in the form: The graph of any quadratic function is a parabola. Can anyone give a real life example of a parabola?

It doesn’t get more real life than this…

All parabolas have an axis of symmetry, meaning if we were to fold a parabola along its axis of symmetry, the portions of the parabola on either side of the line would match. The equation of the axis of symmetry will also be x= a constant.

The vertex of a parabola is the point where the graph changes direction. It is either the maximum or minimum point of function, depending if the parabola is opens upwards or downwards.

The equation of the axis of symmetry is: The value for x in the axis of symmetry is also the x coordinate of the vertex. The y-intercept of the parabola will be the value when x=0, which is the ordered pair (0,c).

Steps for graphing a parabola using a table of values:

Example 1: a) Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b) Make a table of values that include the vertex. c) Use this information to graph the function. Let’s graph!

1)

2)

3)

Try these. 4) 5)

Keep in mind that when the “a” coefficient is greater than 0, the parabola will open upwards. As a result, this type of parabola will have a minimum value. A parabola with an “a” coefficient less than 0 opens downwards, and thus has a maximum value. The minimum or maximum value will be the y-coordinate of the vertex of the parabola.

Example 2: Determine whether the function has a maximum or a minimum value. State the maximum or minimum value. 1)

2)

Try these. 3) 4)