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9.1 Graphing Quadratic Equations

9.1 Graphing Quadratic Equations. Objective: Analyze the characteristics of graphs of quadratic functions Graph quadratic functions. Quadratic Function. A nonlinear function Form f(x) = ax 2 + bx + c The form above is called standard form. Parabola. The shape of a quadratic function.

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9.1 Graphing Quadratic Equations

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  1. 9.1 Graphing Quadratic Equations Objective: Analyze the characteristics of graphs of quadratic functions Graph quadratic functions

  2. Quadratic Function • A nonlinear function • Form f(x) = ax2 + bx + c • The form above is called standard form

  3. Parabola • The shape of a quadratic function. • Form: ax2 + bx + c

  4. Parabolas throughout the world

  5. Axis of Symmetry • Intersects the parabola at only one point. • A line that cuts the parabola in half. • Formula: Find equation

  6. Vertex • The point where the axis of symmetry intersects a parabola

  7. Find the equation of the Axis of Symmetry Formula

  8. Find the vertex for the equation

  9. Find the y-intercept for the equation

  10. Minimum = Smile • The lowest point on the graph • If a > 0, the graph of y= ax2 + bx + c, opens upward • If a > 0 the parabola has a minimum

  11. Maximum = Frown • The highest point on the graph • If a < 0 the graph of y= ax2 + bx + c, open downward • If a < 0, the parabola has a maximum

  12. Identify The Maximum or Minimum • Determine If a < 0 Maximum, If a > 0 Minimum • Find the vertex of your equation. • The y- coordinate is your Maximum or Minimum value

  13. Find the Maximum or Minimum and State the Domain and Range

  14. Homework • Page 532 #34, 38, 44 , 46

  15. What is the Vertex of the parabola? Is it a Max or min?

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