Cheatography
https://cheatography.com
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 = y2y1/x2x1 
yintercepy 
b 
Slope intercept form 
f(x) = mx + b 
Pointslope form 
yy1 = y2y1/x2x1 (xx1) 
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 xaxis 

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:
a^{3} + b^{3} = (a+b) (a^{2}  ab + b^{2}) 


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) = 2x^{3}  6x^{2} + 10 
Exponents 
Always positive exponents and no fractional exponents 
Coefficients 
2, 6 
Constant coefficient/Constant term 
10 
Leading coefficient 
2 
Leading term 
2x^{3} 
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)
