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Unit 4 Quadratics

Unit 4 Quadratics. Quadratic Functions. Any function that can be written in the form. Put in Standard Form and Find a, b, and c. Is it quadratic?. Quadratic Functions. Graph forms a parabola concave up concave down. or. Determine whether a parabola opens up or down.

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Unit 4 Quadratics

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  1. Unit 4Quadratics

  2. Quadratic Functions • Any function that can be written in the form

  3. Put in Standard Form and Find a, b, and c

  4. Is it quadratic?

  5. Quadratic Functions • Graph forms a parabola concave up concave down or

  6. Determine whether a parabola opens up or down

  7. Up or Down?Max or Min?

  8. Using a graphing calculator, find vertex, line of symmetry, max/min, and zeros and where the function increases and decreases..

  9. Another

  10. And another

  11. Average Rate of Change of a Quadratic

  12. Example

  13. Finding Average Rate of Change

  14. Average Rate of Change

  15. To find the axis of symmetry • When

  16. Find the vertex and los

  17. Vertex (h,k) form of a Quadratic • Standard Form:

  18. Parent Function

  19. Transformations • You can tell what the graph of the quadratic will look like if the eq. is in (h,k) form

  20. Sketch the graph

  21. Sketch the graph

  22. Sketch the graph

  23. Sketch the graph

  24. Sketch the graph

  25. Identifying Important Parts on Calculator • 2nd calc—then select max or min

  26. Completing the Square • Used to go from standard form to (h,k) form or to get the equation in the form of a perfect square to solve • Steps: • Move the constant • Factor out the # in front of x2 • Take ½ of middle term and square it • Write in factored form for the perfect sq. trinomial • Add to both sides (multiply by # in front) • Move constant back to get in (h,k) form

  27. Solve

  28. Solve

  29. Complete the Square

  30. Complete the Square

  31. Example

  32. Example

  33. Example

  34. Solving Quadratics • You can solve by graphing, factoring, square root method, and quadratic formula • Solutions, roots, or zeros

  35. Solving by Graphing • Graph the parabola • Look for where is crosses the x-axis (where y=0) • May have 2 real, 1 real, or no real solutions (Show on calculator) Review finding the vertex

  36. Solve the following by graphing

  37. Solving Quadratics by Factoring • Factor the quadratic • Set each factor that contains a variable equal to zero and solve (zero product property)

  38. More solving by factoring

  39. You Try

  40. Writing the Quadratic Eq. • Write the quadratic with the given roots of ½ and -5

  41. Write the quadratic with • Roots of 2/3 and -2

  42. More about solving • Graphing—not always best unless you have exact answers • Factoring—not every polynomial can be factored • Quadratic Formula—always works • Square Root method—may have to complete the square first

  43. Solving using Quadratic formula • Must be in standard form • Identify a, b, and c

  44. Examples

  45. Examples

  46. Examples

  47. Examples

  48. Discriminant • Used to identify the “type” of solutions you will have (without having to solve)

  49. If the discriminant is… • A perfect square---2 rational solutions • A non-perfect square—2 irrational sol. • Zero—1 rational sol. • Negative—2 complex sol.

  50. Identify the nature of the solution

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