Algebra Review Flashcards
Coefficient
Number that is multiplied by a variable (ex. 2 in 2x)
Constant
Term with no variable
Identity
Statement of equality between two algebraic expressions that is true for all possible variables involved
Equation
Statement of equality between two algebraic expressions that is true for only certain values of the variables involved
x^-a
1/(x^a)
(x^a)(x^b) =
x^(a+b)
(x^a)/(x^b) =
x^(a-b)
x^0 =
1
(x^a)(y^a) =
(xy)^a
(x/y)^a =
(x^a)/(y^a)
(x^a)^b =
x^ab
(x+y)/a =
(x/a) + (y/a)
When dividing an inequality by a negative number, the direction of the inequality is…
Reversed.
When dividing an inequality by a positive number, the direction of the inequality is…
Preserved.
Domain (function)
Set of all permissible inputs of that function
Simple interest
Based on the initial deposit, or principal (which serves as the amount on which interest is computed)
V = P (1+(rt/100))
Where r is the interest rate (ex 6%, r=0.06) and t is time in years (ex 6 months, t=0.5)
Compound interest
Interest added to the principal (initial deposit) at some time interval (annually, quarterly, or monthly). Interest is then earned on each new principal
V = P (1+(r/100))^t
Compound interest at an annual interest rate of r percent, compounded n times per year
V = P ( 1 + (r/100n))^nt
To find the distance between two points on a graph…
Construct a right triangle and use Pythagorean theory to find hypotenuse
Linear equation (graphing)
y = mx + b m = slope b = y-intercept
Slope
Rise over run
X2-X1
Two lines are perpendicular if…
Slopes are negative reciprocal of one another
Ex. y=2x+5 and y=-1/2x +9
Finding y-intercept
Insert (x,y) point into equation if you know slope. Then solve for b
Equation system solution result:
Point at which the two lines intersect
Reflection of point (a,b) across the line y=x
Point (b,a)
Reflection of any line across the line y=x is also found by…
Interchanging x and y.
Ex. y=2x+5
Change to x= 2y + 5 and solve for y to find reflection line.
Solutions of the equation ax^2+bx+c are the ________ of the parabola
X-intercepts
To solve for x intercepts of parabola,
Set equation so that y=0, then solve.
To solve for y-intercept of parabola,
Set equation so that x=0, then solve.
(x-a)^2 + (x-b)^2 = r^2
Circle with a center of (a,b) and radius r
To find intersection points of the function of a line and a parabolic function,
Set them equal to one another, then move everything to one side (set equal to 0). Then use a, b, and c values to solve with quadratic equation. Will yield x-coordinates of the two solutions. Then insert both x coordinates into simpler function and solve. Will yield y-coordinates.
Reflection of function y= h(x) about the x-axis is always…
y= -h(x)
Graph of h(x)+c is the graph of h(x)
Shifted upward by c units
Graph of h(x)-c is the graph of h(x)
Shifted downward by c units
Graph of h(x+c) is the graph of h(x)
Shifted to the left by c units
Graph of h(x-c) is the graph of h(x)
Shifted to the right by c units
