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SAT stuff

QuestionAnswer
What is the mean? its the same thing as the average
median put the numbers in order, pick the middle: if there are two middle numbers, then find the average of these two numbers
mode the number that appears most often
How to know if sm is a quadratic function given a table of x and y values 1. Find the first differences (subtract the y values) 2. Find the second differences and if the 2nd difference is constant (the same number over and over) it is a quadratic → on a graph they make a U or upside down U shape
quadratic function formula y = a(x-h)^2 + k vertex= (h, k) -PARABOLA
natural numbers numbers you can count w/ (excludes zero)
whole numbers natural numbers + zero
Integers whole numbers + negatives
Rational numbers numbers that can be written as a/b (repeating decimals count)
irrational numbers cannot be written as a fraction, decimals that go on forever without repeating
factoring out a common binomial 57x(x+b) + a (x + b)=0, factor out x+b → (x+b)(57x+a)=0
formula of a circle (x - h)² + (y - k)² = r² (h,k): The coordinates of the circle's center. (r): The radius (distance from the center to any point on the edge).
completing the square X^2 + 6x +3 = 9 → X^2 + 6x + __ + 3 - 9 = 0 _____ = (6/2)^2 = 9 X^2 + 6x + 9 + 3 - 9 (x+3)^2 - 6 6 = (x+3)^2 +or- rad6 = x+3
when to put the plus or minus symbol in front of your answer x^2 = A x = + or - radA
Given two points, how to find the y-intercept find the slope and then use point-slope form OR you can use y-intercept form by plugging the m and one point into the equation y = mx +b
compound interest. A = P (1 + r/n)^nt → A = final amount, P = principle amount, r = annual interest rate (decimal) n = number of times compounded per year, t = yrs -you earn interest on the original money and on the interest you've already earned
Continuous compounding A = Pe^rt -instead of interest being added yearly monthly, or daily, it's constantly added every instant -growth happens continuously
Simple interest I = Prt → interest earned, → Total amount = A = P + I -you earn interest only on the original amount, you increase by the same amount each time
Percent growth A = P (1 + r)^t
Percent Decay P(1-r)^t
Exponential models y = a(b)^x → a = starting value, b>1: growth, 0 < b< 1: decay x = time or number of periods (how many times the growth or decay happens)
Present value PV = FV/[(1+r)^n] -present value = amount of $ needed today to end w/ a certain amount in the future -FV = future value r = interest rate per period n= # of periods -anything that changes by the same percent or same multiplier each period
Distance formula rad[(x-x)^2+(y-y)^2]
midpoint [ (x + x)/2, (y+y)/2]
quadratic formula x = -b +or- rad(b^2 - 4ac) all divided by 2a
Vertex formula b/2a
Vieta’s formula if you have a quadratic equation in standard form (ax^2 + bx +c = 0), then the sum of the solutions is -b/a and the product of the solutions is c/a
When given two expressions that equal each other, sometimes you move everything to one side and set equal to zero, and sometimes you simply each side individually. Move to one side→ solving for x or y, Simplify separately → two expressions are equivalent and ask for a constant like r, a, or k
-given an absolute value equation |a+x| = c and |a+x| = -c
Discriminant > 0 two solutions
Discriminant < 0 no real solutions
Discriminant = 0 one solution
FOIL first, outside, inside, last (a+b)(c+d) → a * c, a*d, b*c, b*d
If an equation is linear... -both the x and y variable an exponent of 1 and that x and y are not multiplied together -it can be written as a line on a graph
given a function, f(x) and y are the same thing, so when asked to find when f(x) is 0 find where the graph intersects the x-axis (AKA when y = 0) -also, these points are the roots, zeros, or solutions
 

 



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