# MathStudyGuide

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1. interval notation
use of parentheses and brackets, brackets if <= or >=, to denote the domain or range
2. function
one value of x yields only one result
3. domain
the set of x values that can satisfy a function
4. range
the set of y values that can satisfy a function
5. slope formula
(Y2-Y1)/(X2-X1)
6. slope intercept form
y=mx+b
7. standard form
AX+BY=C
8. slope in standard form
-B/A
9. point-slope form
Y-Y1=m(X-X1)
10. linear equation
equation with one or two variables, each of which has a power of 1
11. how to solve for intercept in two variable equation
plug in zero for other variable
12. regression
equation of best fit; linear, quadratic, constant, cubic, etc.
13. step function
closed dots-on 'line'; open dots-above next closed dot with same y value of last point
14. linear combination
eliminate one variable by addition/subtraction of equations
15. substitution
solve for one variable in terms of another or others
16. bounded
finite number of solutions
17. unbounded
infinitely many solutions
18. linear program theory
optimization of a linear function will occur at the vertex of the feasible region
19. an A by B matrix has how many columns?
B
20. an A by B matrix has how many rows?
A
21. how to find inverse of a matrix
(matrix name)^(-1)
22. how to find determinant
2nd>matrix>math>det(matrix name)
23. augmented matrix dimensions
A by A+1
24. augmented matrix
each row has coefficients of variables in order, 'answer' in last column. each column has all of x values, all of y values, etc.
25. solve an augmented matrix
row-reduced echelon function
26. answer of an augmented matrix
identity matrix + one column with solutions
27. double check entered matrices
double check entered matrices
28. what kinds of matrices can be added?
identical dimensions
29. what kind of matrices can be multiplied?
inside dimensions identical (A by B and B by A, but not A by B and A by B)
30. when multiplying to matrices of dimensions A by B and B by A, what will be the dimensions of the product?
B by B
31. to find area of triangle with 3 points given, how can one find the area using matrices?
first two columns are values given, third is all ones; absolute value of determinant/2
32. when matrix A is multiplied by its inverse, what is the result?
identity matrix
33. cramer's rule
denominator of each solution is determinant of coefficent matrix; numerator is determinant of identical matrix except with 'answers' instead of coefficients of variable solving for
34. vertex of parabola
point at most extreme value of y
35. do roots go in the denominator?
NO!!!!
36. completing the square
square sum or difference of x and (coefficient of x/2), add square to other side; solve
37. vertex form
(x-(x of vertex)^2+(y of vertex)
38. discriminant
b^2- 4ac, NOT the square root of this