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Graphing Quadratic Functions – Standard Form

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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  1. 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.

  2. 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.

  3. 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:

  4. Example 2 Put the function in the form of … The vertex is given by:

  5. 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:

  6. Example 3 The vertex is given by:

  7. 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.

  8. 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

  9. Example 4 Sketch the graph of the following function:

  10. Start the sketch of the graph with what we have so far. The parabola is face up

  11. x-intercepts y-intercept

  12. y-intercept x-intercepts • Plot the intercepts

  13. Sketch the parabola, using the points and axis of symmetry.

  14. Example 5 Sketch the graph of the following function:

  15. Start the sketch of the graph with what we have so far. The parabola is face down

  16. x-intercepts

  17. x-intercepts • Plot the x-intercepts

  18. y-intercept

  19. Skip plotting the y-intercept since it is off of the graph. • Sketch the parabola, using the points and axis of symmetry.

  20. END OF PRESENTATION Click to rerun the slideshow.

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