Graphing Quadratic Functions General Form It is assumed

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Graphing Quadratic Functions – General Form • It is assumed that you have already

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.

Standard Form of a Quadratic Function General Form of a Quadratic Function

Standard Form of a Quadratic Function General Form of a Quadratic Function

Graphing a Quadratic Function in Standard Form Face Up Face Down Narrow Wide Vertex

Graphing a Quadratic Function in Standard Form Face Up Face Down Narrow Wide Vertex Axis of symmetry

Plotting an Extra Point when Graphing Quadratics Narrow Choose a value for x 1

Plotting an Extra Point when Graphing Quadratics Narrow Choose a value for x 1 unit away from the vertex. Wide Choose a value for x more than 1 unit away from the vertex

Vertex of the Graph of a Quadratic Function in General Form • Given the

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

 • There are two other helpful concepts for graphing a quadratic function that

• 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 …

Thus, the vertex of the graph of the quadratic function in general form is

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.

Summary for Graphing Quadratics in General Form Face Up Vertex Face Down Narrow Wide

Summary for Graphing Quadratics in General Form Face Up Vertex Face Down Narrow Wide Axis of symmetry

 • Example: Sketch the graph of the given quadratic function. Face down Narrow

• Example: Sketch the graph of the given quadratic function. Face down Narrow Vertex:

Vertex

Vertex

Axis of Symmetry: x = x-value of vertex Point: since the parabola is narrow,

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.

Summary: Function: Face down Narrow Axis: Point:

Summary: Function: Face down Narrow Axis: Point:

Plot the vertex Plot the axis: Plot the point: Draw the branch of the

Plot the vertex Plot the axis: Plot the point: Draw the branch of the parabola on the right side of the axis. Use symmetry to draw the left branch. Label