Graphing Quadratic Functions General Form

1
Graphing Quadratic Functions General Form

• It is assumed that you have already viewed the
  previous three slide shows titled
• Graphing Quadratic Functions Concept
• Graphing Quadratic Functions Standard Form
• Graphing Quadratic Functions Converting
  General Form To Standard Form

• The next three pages are summaries from those
  shows, and are important to understanding this
  module.

2
General Form of a Quadratic Function
Standard Form of a Quadratic Function
3
Graphing a Quadratic Function in Standard Form
Vertex
Face Up
Face Down
Axis of symmetry
Narrow
Wide
4
Plotting an Extra Point when Graphing Quadratics
Choose a value for x 1 unit away from the vertex.
Choose a value for x more than 1 unit away from
the vertex
5
Vertex of the Graph of a Quadratic Function in
General Form

• Given the general form of a quadratic function

the x-value of the vertex is given by
6

• There are two other helpful concepts for
  graphing a quadratic function that is in general
  form.

• Concept 1

We already know that the x-value of the vertex is
given by
The y-value of the vertex is given by
7
Thus, the vertex of the graph of the quadratic
function in general form is given by

• Concept 2

The a of the general form is the same value as
the a in the standard form.
This means that the a in the general form can be
used to determine the face up/face down and
narrow/wide behavior, just as it did in the
standard form.
8
Summary for Graphing Quadratics in General Form
Vertex
Face Up
Face Down
Narrow
Axis of symmetry
Wide
9

• Example

Sketch the graph of the given quadratic function.
Face down
Narrow
Vertex
10
(No Transcript)
11
Axis of Symmetry x x-value of vertex
Point since the parabola is narrow, use an
x-value that is only one unit from the vertex.
12
Summary
Face down
Narrow
13
Draw the branch of the parabola on the right side
of the axis.
Use symmetry to draw the left branch.
Label
14
END OF PRESENTATION
Click to rerun the slideshow.