Cheatography

# Algebra Cheat Sheet (DRAFT) by Lady_Notenook

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)

 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)