11x1 t11 01 graphing quadratics

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  • 1. The Quadratic Polynomial and the Parabola
  • 2. The Quadratic Polynomial and the Parabola Quadratic polynomial
  • 3. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c
  • 4. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function
  • 5. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c
  • 6. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation
  • 7. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0
  • 8. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients
  • 9. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c
  • 10. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate
  • 11. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x
  • 12. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots
  • 13. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation
  • 14. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation Zeroes
  • 15. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function
  • 16. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0
  • 17. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0 x2 1 0 x2 1
  • 18. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0 x2 1 0 x2 1 x 1
  • 19. The Quadratic Polynomial and the Parabola Quadratic polynomial ax 2 bx c Quadratic function y ax 2 bx c Quadratic equation ax 2 bx c 0 Coefficients a, b, c Indeterminate x Roots Solutions to the quadratic equation Zeroes x intercepts of the quadratic function e.g. Find the roots of x 2 1 0 x2 1 0 x2 1 x 1 the roots are x 1 and x 1
  • 20. Graphing Quadratics
  • 21. Graphing Quadratics The graph of a quadratic function is a parabola.
  • 22. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c
  • 23. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c a
  • 24. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c y a x
  • 25. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c y a x a0
  • 26. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c y a x a0 concave up
  • 27. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c y y a x x a0 concave up
  • 28. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c y y a x x a0 a0 concave up
  • 29. Graphing Quadratics The graph of a quadratic function is a parabola. y ax 2 bx c y y a x x a0 a0 concave up concave down
  • 30. Graphing Quadratics The graph of a quadratic function is a parabola. y