Key Equations and Concepts in Mathematics
Parallel = Original equation. PP = – Reciprocal
x = (-b ± √(b^2 – 4ac)) / (2a), complex solutions. Vertex = (-b) / (2a)
(x/2)^2. If a > 0, then the parabola opens up.
Parabola form = a(x – h)^2 + k. If a < 0, then the parabola opens down.
P = 2L + 2W
x + x + z = y
A = L * W
N = odd and an > 0 = Falls Left + Rises Right
N = odd and an < 0 = Rises Left + Falls Right
N = Even and an > 0 = Rises Left + Rises Right
N = Even and an < 0 = Falls Left + Falls Right
Rational zero = P/Q
Factor = x – zero
Quotient = Synthetic division
Distance = √((X2 – X1)^2 + (Y2 – Y1)^2)
Reflection about the x-axis of the graph y = x^2 and y = -x^2
Symmetry to the x-axis: (x, -y) is on the graph when (x, y) is. Test for symmetry: In the equation, leave x alone and replace y with -y. If you get the same equation, it is symmetric to the x-axis.
Symmetry to the y-axis: (-x, y) is on the graph when (x, y) is. Test for symmetry: In the equation, replace x with -x. If the equation is the same, it is symmetric to the y-axis.
Symmetry to the line y = x: (y, x) is on the graph when (x, y) is. Test for symmetry: Interchange x and y. If the equation is the same, then it is symmetric to the line y = x.
Symmetry to the origin: (-x, -y) is on the graph when (x, y) is. Test for symmetry: Replace x with -x and y with -y. If the equation is the same, then it is symmetric to the origin.
If a zero has odd multiplicity, then the graph crosses the x-axis at the zero.
If a zero has even multiplicity, then the graph touches the x-axis at the zero.
If N < M, no HA (Horizontal Asymptote)
Difference Quotient
=
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y = g(1/2x) divide by 1/2 or multiply by 2 = Horizontal. C > 1 shrink, 0 < C < 1 stretch
y = 1/2g(x) means Multiply by 1/2 = Vertical. C > 1 stretch, 0 < C < 1 shrink
Linear Function: f(x) = mx + b = slanted line
Square Function: f(x) = x^2 = U
Cube Function: f(x) = x^3 = Z
Square Root Function: f(x) = √(x) = Hook
Absolute Value Function: f(x) = |x| = V
Reciprocal Function: f(x) = 1/x = >
The Cube Root Function: f(x) = ∛x = S
Step 1: Enter the data Calculator: STAT, EDIT Enter the two columns of data. Note: To clear old data from a column quickly, move the cursor to the top of the column (on top of L1 or L2, etc.), hit CLEAR and then ENTER.
Step 2: Find the line of regression Calculator: STAT, arrow right to CALC, arrow down to #4 (LinReg (ax + b)), ENTER or CALCULATE (to return to the home screen), and ENTER again to calculate. Important Note: When calculating the line of regression, we are sometimes asked to find the correlation coefficient, denoted with an r. We need to set up the calculator so that it will show r. You should only need to do this on your calculator once, but you may also need to do it on any calculator you use in the test center. Turning on the correlation coefficient: 1. Hit the “Catalog” key on your calculator (2nd , the number zero). 2. Scroll down to “Diagnostic On” 3. Hit “Enter” and it should appear on the homescreen. 4. Hit “Enter” again, and you are done. Remember: The closer the r is to 1 or -1, the closer the data fits a line.
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