QUADRATICS
By: Indroop Bassi
Table of Contents
Introduction:
- Parabolas
- Second Differences
- Transformations
Types of Equations:
- Vertex Form
- Factored Form
- Standard Form
Vertex Form
- Equation In Vertex Form
- Mapping Notation
- Determine the Equation From a Graph
Factored Form
- Multiplying Binomials
- Special Products (binomials)
- GCF and Factor by Grouping
- Simple Factoring
- Factoring Quadratic Expression/Special Cases
- Solve by Factoring
- Graphing Factored Form
Standard Form
- Quadratic Formula
- Discriminant
- Completing the square
- Graphing from standard form
Word Problems:
- Height
- Profit
- Geometry
- Number Problems
- Economic
Introduction
Second Differences
Parabolas
Axis of Symmetry: line that splits the parabola in half (x value)
Optimal Value: y value, can be a MAXIMUM or MINIMUM value
x intercepts: the zeroes
y intercepts: graph crosses y axis
Transformations
The (-h) is the horizontal translation. It moves the parabola either to the LEFT or RIGHT. (when it's positive, moves to left. When it's negative, moves to right)
The (k) is the vertical translation. It moves the parabola UP or DOWN. When k is negative, it moves down. When k is positive, it moves up.
The (a) is the vertical stretch and is reflected in the x-axis if there is a negative sign. It also stretches the parabola.
Vertex (h,k)
Once you know the vertex, you can use the step pattern to find the rest of the points to complete the graph.
Types of Equations
2. Standard Form: y= ax²+bx+c
3. Factored Form: y= a(x-r)(x-s)
Vertex Form
Solving Given Vertex Form
Isolating for x
1. Transfer -50 to the other side of the equal sign. Moving it over changes it to +50
2. Divide both sides by 2
3. Square root both sides of the equation to get rid of ²
4. Transfer -5 to the other side of the equal sign to have x by itself. (Make sure -5 changes to +5 after moving it to the other side)
5. Solve
Graphing Vertex Form
Factored Form
Expanding (Factored to Standard)
F = First Term
O = Outside Term
I = Inside Term
L = Last Term
Simple Trinomials
Complex Trinomials
Common Factoring
Specials Cases (Perfect Square & Difference of Squares)
Factoring by Grouping
Graphing Factored Form
Standard Form
Solving Using Quadratic Equation
1. Find the value of a,b & c with the equation provided
2. Use the quadratic formula to sub in the values
3. Solve to find x intercepts
Discriminant
Completing the Square
Graphing Standard Form
Word Problems
Height
Profit
Area
Number Problem
Economic
2. Use revenue formula
3. Write the equation
4. Solve