Quadratic Relations
Final Submission || Harman Virk
Table of Contents
- The Parabola
Graphing Vertex Form:
- First and Second Differences
- Identifying Transformations of a Parabola
- Word Problem
Factored Form:
- Video of Factoring
- Different Types of Factoring and Examples
- Factoring to determine x-intercepts
- Word Problem
Standard Form:
- Completing the Square
- Quadratic Formula
- The Discriminant
- Word Problem
Conclusion:
- Assessment
- Reflection
The Parabola
- Parabolas can open up or down
- The zero of a parabola is where the graph crosses the x-axis
- "Zeros" can also be called "x-intercepts" or "roots"
- The axis of symmetry divides the parabola into two equal halves
- The vertex of a parabola is the point where the axis of symmetry and the parabola meet. It is the point where the parabola is at its maximum or minimum value.
- The optimal value is the value of the y co-ordinate of the vertex
- The y-intercept of a parabola is where the graph crosses the y-axis
Graphing Vertex Form
First & Second Differences
Identifying Transformations of a Parabola
If a > 0, the parabola opens up.
If a < 0, the parabola opens down.
If -1 < a < 1, the parabola is vertically compressed.
If a > 1 or a < -1 the parabola is vertically stretched.
The 'k' value
If k > 0, the vertex moves up by k units.
If k < 0, the vertex moves down by k units.
The 'h' value
If h > 0, the vertex moves to the right by h units.
If h < 0, the vertex moves to the left by h units.
Word problem
Factored form
Types of Factoring
Different Types of Factoring & Examples
- The greatest common factor (GCF) is the largest integer that divides evenly into each of a given set of numbers.
- When factoring polynomial expressions we must find the greatest common factor.
- We look for the greatest common numerical factor, and for the variable with the highest degree of the variable common to each term.
- We are looking for a whole number factor
- A simple trinomial is a quadratic where 'a' = 1
- Given a quadratic in standard form, you can factor to get factored form
- 'a' does not equal 1
- Always look at the common factor first when factoring trinomial
- Not all quadratic expressions can be factored.
- Always look for a common factor first when factoring a trinomial
- We have two different terms
Factoring to determine x-intercepts
1) Replacing y with 0 and factoring the quadratic
2) Setting each bracket = 0 and solving for x
0 = (x + 9) (x + 3)
x + 9 = 0 --> x = -9
x + 3 = 0 --> x = -3
The x-intercepts are -3 and -9
Word Problem
Standard Form
Completing the Square
y = ax^2 + bx + c ----> y = a (x - h)^2 + k
Quadratic Formula
The discriminant
When D < 0, there will be zero solutions.
When D = 0, there will be one solution.