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Algebra Cheat Sheet (DRAFT) by

Linear Functions Quadratic function Polynomial Functions

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Linear Functions

Standa­rd/­General form:
f(x) = ax + b
Slope/rate of change
a/m = y2-y1/­x2-x1
y-inte­rcepy
b
Slope intercept form
f(x) = mx + b
Point-­slope form
y-y1 = y2-y1/­x2-x1 (x-x1)
Variable occurs to the first power only
The graph is a line
Constant rate of change
Positive rate of change
Slope Upward
Negative rate of change
Slope Downward

Effects of Changing h and k

vertex form: (h, k)
Changing h
x = h; horizontal shift
Changing k
y = k; vertical shift

How to solve Poly­nomial Functi­ons

 
1. Factor out (no exponent is inside the parent­hesis)
 
2. Set the function equal to zero
 
3. Solve for x
 
4. Find Multip­licity
 
5. Find x and y intercept. Use 0, if imaginary use 2 numbers that are symmetric to each other
 
6. Plot out the x you solve on step 3 sa x-axis
 
7. Plot the x and y intercepts on step 5
 
7 Check if tama ang graph using ang leadig coeffi­cient

Create Quadratic func. with the Vertex and points

1. Substitute the vertex to the function
2. Substitute x and y intercept
3. Solve for a

Formula:

a3 + b3 = (a+b) (a2 - ab + b2)
 

Quadratic Functions

General form
f(x) = ax + bx + c
Standard form
f(x) = a(x - h) + k
Vertex
(h, k)
Polynomial function of degree 2
Graph of f is a parabola
Parabola opens upward
a > 0 (+) : minimum
parabola opens downward
a < 0 (-) : maximum

How to graph Quadratic Functions

1. Expressing in standard form by completing the square or using (x = -b/2a
2. Find Vertex
3. Identify max/min
4. Find x and y intercept
5. Plot Vertex and points
6. Find domain ad range Note: Domain is always real number

Even Coeffi­cient Graph

Same Direction sa start and end If Positive: Upward If Negative: Downward

Odd Coeffi­cient

Opposite Directions If Postiv­e:a­sce­nding, If Negative: descending
  

Polynomial Function

Example sa form
f(x) = 2x3 - 6x2 + 10
Exponents
Always positive exponents and no fractional exponents
Coeffi­cients
2, -6
Constant coeffi­cie­nt/­Con­stant term
10
Leading coeffi­cient
2
Leading term
2x3
It is contin­uous; graph has no breaks or holes
Note: Dapat always sunod ang mga terms depende sa # of degree or exponents. If kulangan butangan ug 0 ang exponent
Higher exponent (even)
Steeper, flatter
Higher exponent (odd)
wider

Remainder Theorem

If a polynomial p(x) is divided by the binomial x - a, the remainder obtained is p(a)

Factor Theorem

C is a zero of p if and only x - c is a factor of P(x)