chapter 2 vocab

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chapter 2 vocab by Mind Map: chapter 2 vocab

1. quadratic function- a function written in the form ax^2+bx+c.

2. An example of a quadratic function would be 3x^2-6x+5

3. Parabola- A parabola is the U shaped curve.

4. An example of a Parabola would be X^2

5. Vertex(of a parabola)- the highest or lowest point on a parabola.

6. An example of a vertex on a parabola. If you have the equation 3(x-6)^2+8, the vertex would be (6,8)

7. Completing the square- A process used to form a perfect square trinomial.

8. An example of completing the square would be x^2+4x. To complete the square add (b/2)^2 and you would get (4/2)^2, which equals 4. Then you add four to the equation to get x^2+4x+4.

9. Axis of Symmetry- The line through the vertex of a parabola

10. An example would be if you have the equation 3(x-6)^2+k, the vertex would be H, which is equal to 6.

11. Zero of a function- The value of input that makes the output

12. An example of zero of a function would be the x- intercepts.

13. Quadratic functions have two x intercepts.

14. Trinomial- A polynomial with 3 terms

15. An example of a trinomial would be x^2+5x-4

16. Vertex Form- A quadratic function written in the form A(x-h)^2+k

17. An example of this would be 3(x-7)^2+6

18. Standard Form- A form of linear equation Ax+By=c

19. An example of standard form would be 3x+7y=9

20. Root of an equation- Any value of the variable that makes the equation true

21. An example of a root of an equation would be if the roots are -2 and -3, the equation would have to be (x+2) (x+3) to make the equation true.

22. Minimum value- The value of the vertex when a parabola opens downward.

23. An example of minimum value. If you have a function of 3x^2+2x+1, the minimum would be 2/3.

24. Maximum value- The y value of the vertex when a parabola opens downward

25. An example of maximum value. If you have a function of -2x^2-4x-2. The maximum value would be 0.

26. Imaginary Number- The square root of a negative number, written in the form bi, where b is a real number and i is an imaginary unit.

27. An example of an imaginary number would be 4 times the square root of -25 which would equal 20i.

28. Imaginary Unit- The unit in imaginary number system.

29. An example of the imaginary unit would be the square root of -1.

30. Complex Number- Any number that can be written as a+bi, where a and b are real numbers and i equals the square root of -1.

31. An example of a complex number would be 2+3i.

32. Real Part- For a complex number in the form of a+bi, a is the real part

33. An example of a real part. From the complex number of 4+7i, 4 would be the real part.

34. Imaginary Part- For a complex number in the form of a+bi, b would be the imaginary part.

35. An example of an imaginary part. If you have the equation 2+5i, 5 would be the imaginary part.

36. Complex Conjugate- Two complex numbers that have the same real part and imaginary part but opposite signs.(a+bi) to (a-bi).

37. An example of complex conjugate. The complex conjugate of 2+4i would be 2-4i.

38. Discriminant- The discriminant of the quadratic equation ax^2+bx+c=0 is b^2-4ac

39. An example of discriminant. If you have the equation 3x^2+5x+8, the discriminant would be 3x^2-4(5)(8).

40. Quadratic Model- A quadratic function used to represent a set of data

41. An example of a quadratic model would be -16x^2+64x+4

42. Quadratic Regression- A statistical method used to fit a quadratic model to a given set of data.