Graphing Quadratic Functions – Standard Form

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# Graphing Quadratic Functions – Standard Form - PowerPoint PPT Presentation

Graphing Quadratic Functions – Standard Form. It is assumed that you have already viewed the previous slide show titled Graphing Quadratic Functions – Concept . The summary of the Concept slide show is given again on the next page. Face Down. Face Up. Axis of symmetry:.

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## Graphing Quadratic Functions – Standard Form

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Presentation Transcript

Graphing Quadratic Functions – Standard Form

• It is assumed that you have already viewed the previous slide show titled
• Graphing Quadratic Functions – Concept.
• The summary of the Concept slide show is given again on the next page.

Face Down

Face Up

• Axis of symmetry:

x-int: y = f (x)= 0

and solve for x.

y-int: x =0

and solve for y.

SUMMARY

• The graph of a quadratic function in called a parabola.
• The maximum or minimum y-value of a quadratic occurs at the vertex.

The vertex is given by V(h,k).

• Example 1

The vertex is given by:

Example 2

Put the function in the form of …

The vertex is given by:

Here is an easier way to work the last problem:

For the h value, take the opposite sign …

For the k value, take the same sign …

The vertex is given by:

Example 3

The vertex is given by:

Recall that the Axis of Symmetry has the equation

Since the vertex of the standard quadratic function given by

has an x-value of h, we can write the equation of the axis of symmetry as

• Put all of the tools learned so far together to sketch the graph of a quadratic function in standard form.

Vertex

Axis of symmetry

Face Up

Face Down

Sketch the Graph of a Quadratic in Standard Form

x-int: f (x)= 0

and solve for x

y-int: x =0

and solve for y

Draw the parabola

Example 4

Sketch the graph of the following function:

x-intercepts

y-intercept

y-intercept

x-intercepts

• Plot the intercepts

Example 5

Sketch the graph of the following function:

x-intercepts

• Plot the x-intercepts
• Sketch the parabola, using the points and axis of symmetry.

END OF PRESENTATION

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