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Algebra Chapter 10-1 Exploring Quadratic Graphs

Algebra Chapter 10-1 Exploring Quadratic Graphs. Graphing Quadratic Functions NC SCOS 4.02  Graph, factor, and evaluate quadratic functions to solve problems. What you’ll learn. New Vocabulary. quadratic function parabola axis of symmetry vertex minimum maximum. Quadratic Functions.

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Algebra Chapter 10-1 Exploring Quadratic Graphs

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  1. Algebra Chapter 10-1Exploring Quadratic Graphs Graphing Quadratic Functions NC SCOS 4.02  Graph, factor, and evaluate quadratic functions to solve problems.

  2. What you’ll learn

  3. New Vocabulary • quadratic function • parabola • axis of symmetry • vertex • minimum • maximum

  4. Quadratic Functions A QUADRATIC FUNCTION will show up as a U-shaped graph called a PARABOLA. The graph of a quadratic function is a U-shaped curve called a parabola. The graph of y = x2, shown at the right, is a parabola.

  5. Examples of Parabolic Curves • steel cables of a suspension bridge • the supporting arches of some highway • railroad bridges, for it is this shape that naturally holds up a uniformly weighted road surface

  6. A baseball in flight or the arc of water at the lip of a waterfall both follow a parabolic path.

  7. You can fold a parabola so that the two sides match exactly. This property is called symmetry. The highest or lowest point of a parabola is its vertex, which is on the axis of symmetry. • The fold or line that divides the parabola into two matching halves is called the axis of symmetry.

  8. Minimum or Maximum?

  9. Quadratics Notes

  10. The Coefficient and the U

  11. Practice Problems from Text

  12. Graphing the Quadratic Equation Graphing Calculator Graphing By Hand Create a table and graph three to four points. • Math Bits –Parabolas- http://mathbits.com/MathBits/TISection/Algebra1/Parabolas.htm

  13. Online Resources • Video Tutor

  14. Make a table of values and graph DomainRange

  15. If you graph a quadratic function on a piece of paper and fold it down the middle, the two sides will match exactly. The line down the middle of the parabola is called theAXIS OF SYMMETRY. The two symmetric parts are mirror images of each other. The VERTEXis the lowest point (minimum) of a parabola that opens up or the highest point (maximum) of a parabola that opens down.

  16. Glossary of Terms • Quadratic function (p. 510) A function of the form y = ax2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down. • Standard form of a quadratic function (p. 510) The form of a quadratic function written y = ax2 + bx + c, where a ≠ 0. • Parabola (p. 510) The graph of a quadratic function. • Axis of symmetry (p. 511) The line that divides a parabola into two matching halves.

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