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6-1 Graphing Quadratic Functions

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1 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

2 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?

3 It doesn’t get more real life than this…

4 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.

5 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.

6 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).

7 Steps for graphing a parabola using a table of values:

8 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!

9 1)

10 2)

11 3)

12 Try these. 4) 5)

13 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.

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

15 2)

16 Try these. 3) 4)

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