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Quadratic equations

Quadratic equations. Graphing and Solving with x 2. The typical form of a y = x 2 graph:. Quadratic equations Quick Exercise:. Graph the following on the same axes: y = x 2 y = x 2 + 2 y = x 2 - 2x. The form of a y = x 2 + b x + c graph:. General Form of Quadratics.

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Quadratic equations

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  1. Quadratic equations Graphing and Solving with x2

  2. The typical form of a y = x2 graph:

  3. Quadratic equationsQuick Exercise: Graph the following on the same axes: y = x2 y = x2 + 2 y = x2 - 2x

  4. The form of a y = x2 + bx + c graph:

  5. General Form of Quadratics The general form is either: • y = ax2 + bx + c Or • ax2 + bx + c = 0

  6. General Form of Quadratics The general form is either: • y = ax2 + bx + c used for graphing Or • ax2 + bx + c = 0

  7. General Form of Quadratics The general form is either: • y = ax2 + bx + c used for graphing Or • ax2 + bx + c = 0 when solving for x For now, we will stick to when a = 1

  8. Quadratics • The equation for such a modified parabola is called a quadratic. • Quadratics will always have a variable raised to the second power, like x2. • Factoring is one way to find solutions to quadratic equations. 0 = x2 - 6x - 16 0 = (x - 8)(x + 2) x = {-2, 8}

  9. x2 - 2x - 3 = 0 (x - 3)(x + 1) = 0 Set each factor to 0 x - 3 = 0 x = 3 x + 1 = 0 x = -1 x = -1 or x = 3 ¡ A. 1 and 3 ¡ B. -1 and -3 ¡ C. -1 and 3 ¡ D. 1 and -3 ¡ E. 1 and 2 D2. What are the solutions to the quadratic x2 - 2x - 3 = 0?

  10. So what about the y = x2 - 2x - 3 graph?

  11. So what about the y = x2 - 2x - 3 graph?

  12. So what about the y = x2 - 2x - 3 graph? The graph Crosses The x axis Here

  13. So what about the y = x2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1

  14. So what about the y = x2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1 And here

  15. So what about the y = x2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1 And here x = 3

  16. So what about the y = x2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1 And here x = 3 So again we see our solution, x = -1 or x = 3

  17. So what about the y = ax2 + bx + c graph? The graph Crosses The x axis Here x = ? And here x = ? This time we may need to use the quadratic formula

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