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Quadratics Journal

Quadratics Journal. Salvador Amaya. How to factor a polynomial. Find a GCF if possible Divide the whole equation by GCF Multiply a and c Find 2 numbers that multiply to that product and add to b Put both numbers over a Reduce if possible. Example 1.

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Quadratics Journal

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  1. Quadratics Journal Salvador Amaya

  2. How to factor a polynomial • Find a GCF if possible • Divide the whole equation by GCF • Multiply a and c • Find 2 numbers that multiply to that product and add to b • Put both numbers over a • Reduce if possible

  3. Example 1 Factors of are 4 and 3/2

  4. Example 2 Factor of are 4 and 2.

  5. Example 3 Factors of are 1/3 and 3/2

  6. What is a quadratic funtion? • An equation with an squared number • a can’t equal 0 (if it does then it is a linear function • It is a parabola when graphed. • In the form of:

  7. Difference between linear • A linear graphs a line, a quadratic a parabola • A linear is in form y=mx+b, a quadratic in • In a linear function, the y and x don’t have powers

  8. Example 1 • Is this a quadratic or linear function? Why?

  9. It is a linear equation • It has no powers • It is in form y=mx+b • When graphed it is a line:

  10. Example 2 • Which of these equations graphs a parabola? • a. • b. • c.

  11. a.

  12. b.

  13. c. • It is c.

  14. Example 3 • Which equation is quadratic?

  15. It is • Because it has powers on x.

  16. How to graph a quadratic function • Convert, if not already, to graphing form: • A changes the steepness of parabola • If a<0, the parabola goes down of vertex, and is wide • If a>0, the parabola goes up of vertex, and is thin • B moves right or left the parabola vertex • If b is +, vertex goes in the negative side • If b is -, vertex goes in positive side • C moves vertex up or down. • +c moves up • -c moves down

  17. Example 1 • It will graph: thin, it goes up of vertex, vertex is in -3 in x, and it is in -5 in y

  18. Example 2 • It will graph wide, it goes down of vertex, vertex is in -8 in x, and it is in 1 in y

  19. Example 3 • It will graph wide, it goes down of vertex, vertex is in 5 in c, and it is in -6 in y

  20. Solve by graphing • Set y=0 • Graph the function • Make a t-table • Find the vertex using the formula x=-b/2a • Pick 3 points in one side of vertex • Fill in for x in the function to figure out y • Graph the parabola • Reflect the points on the other side of the vertex • Find the x-values where it crosses the x-axis.(solution) • No crossing x-axis=no solution

  21. Solution • It is the number or numbers that fill in for x for the equation to equal 0

  22. Example 1

  23. Example 2

  24. Example 3

  25. Solve by square roots • Get by itself • Make sure there is not an x by itself • Square root both sides and don’t forget the

  26. Example 1

  27. Example 2

  28. Example 3

  29. Solve by factoring • Multiply a and c • Find 2 numbers that multiply to that product and add to b • Put both numbers over a • Reduce if possible • Make those two numbers negative

  30. Example 1 x=-5/8, -3/8

  31. Example 2 x= -1/2, -3

  32. Example 3 x= 3, 5/2

  33. Complete the square • Get a=1 • Find b • Divide b by 2 • Square it • Factor (x + b/2)

  34. Solve completing the square • Get =1 • Get c by itself • Complete the square • Add (b/2) to both sides • Square root both sides • Don’t forget the

  35. Example 1

  36. Example 2

  37. Example 3

  38. Solve with quadratic formula • Formula:

  39. Discriminant • It is the number that appears inside the square root in a quadratic equation. • Ex: Discriminant

  40. Example 1 x= -9/2

  41. Example 2

  42. Example 3

  43. Geometry Review of Algebra Journal  In your own words respond to the following:  Describe how to Factor any polynomial. Give at least 3 examples. _____(0-10 pts) Describe what at quadratic function is. Explain how to tell the difference between a quadratic function and a linear function. Give at least 3 examples. _____(0-10 pts) Describe how to graph a quadratic function. Include a discussion about maximum values, minimum values and vertices. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation by graphing it. What is a solution? Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using square roots. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using factoring. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using Completing the square. Give at least 3 examples. _____(0-10 pts) Describe how to solve a quadratic equation using the Quadratic formula. Explain what a discriminant is. Give at least 3 examples. _____(0-5 pts) Neatness and originality bonus

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