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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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Presentation Transcript
slide1

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.
slide2

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

Graphs of Quadratic Functions

  • The graph of a quadratic function in called a parabola.
  • The maximum or minimum y-value of a quadratic occurs at the vertex.
slide3

A quadratic function in what we will call Standard Form is given by:

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

  • Example 1

The vertex is given by:

slide4

Example 2

Put the function in the form of …

The vertex is given by:

slide5

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:

slide6

Example 3

The vertex is given by:

slide7

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.
slide8

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

slide9

Example 4

Sketch the graph of the following function:

slide11

x-intercepts

y-intercept

slide12

y-intercept

x-intercepts

  • Plot the intercepts
slide14

Example 5

Sketch the graph of the following function:

slide17

x-intercepts

  • Plot the x-intercepts
slide19

Skip plotting the y-intercept since it is off of the graph.

  • Sketch the parabola, using the points and axis of symmetry.
slide20

END OF PRESENTATION

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