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

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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. • A quadratic function in what we will call Standard Form is given by: • The summary of the Concept slide show is given again on the next page.

  2. SUMMARY Vertex Face Up Face Down Axis of symmetry Narrow Wide

  3. Narrow • One more thing is needed before sketching the graph of a quadratic function. A point is plotted to know just how narrow or how wide the graph is. • When the graph is narrow, choose an x-value that is only one unit from the vertex. • In the graph on the right, a good choice would be • x = 1

  4. If the value x = 2 were chosen, then the corresponding y-value would be off the graph.

  5. Wide • When the graph is wide, choose an x-value that is more than one unit from the vertex. • In the graph on the right, a good choice would be • x = 2 or x= 3 • Note that x = 1 would not be very helpful in determining just how wide the graph would be.

  6. Wide Narrow SUMMARY Choose a value for x1 unit away from the vertex. Choose a value for xmore than 1 unit away from the vertex

  7. Example 1: Sketch the graph of the following function:

  8. Plot the vertex: • Draw the axis of symmetry:

  9. Since the graph is narrow, find a point that is only 1 unit from the vertex. • Try x = 3.

  10. Draw the right branch of the parabola using the vertex and the point (3,4). • Now use symmetry to draw the left branch. • Label the axis and important points.

  11. Face Down Vertex: Axis: Wide • Example 2: Sketch the graph of the following function:

  12. Plot the vertex: • Draw the axis of symmetry:

  13. Since the graph is wide, find a point that is more than 1 unit from the vertex (-1,-2). • This problem presents another challenge, which is to avoid fractions if possible.

  14. Therefore, we want to meet two goals: • Select an x-value more than one unit to the right of the vertex (-1,-2). • Avoid fractions. • To meet goal #2, all that is needed is for the quantity that is squared to be divisible by 5. • An x-value of 4 meets this condition, and also satisfies goal #1.

  15. Draw the right branch of the parabola using the vertex and the point (4,-7). • Now use symmetry to draw the left branch. • Label the axis and important points.

  16. END OF PRESENTATION

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