Quadratics - Unit 3
By Amanda Persaud
What Is a Quadratic Relationship?
Quadratic Relationships vs. Linear Relationships
Forms of Quadratic Equations
'a' represents the stretch factor (if there is one).
'b' and 'h' represent the x coordinate of the parabola's vertex/the axis of symmetry.
'c' represents the parabola's y-intercept (if there is any).
'k' represents the y value of the vertex.
'r' and 's' represents the parabola's x-intercepts (if there are any).
Vertex form: y = a(x - h)² + k
X-intercept form: y = a(x - r)(x - s)
Standard form: 0 = ax² + bx + c
To get from y = x² to y = -2(x - 3)² + 1
- Horizontal translation to the right by 3
- Vertical translation up 1
- Vertical flip
- Stretch by a factor of 2
Components of a Quadratic Graph
- Axis of symmetry
The Step Pattern
Factoring and Expanding Quadratic Expressions
Quadratic expressions could be expanded (simplified) by using the distributive property.
Difference of Squares
Standard Form Equations
(x + 4)(x + 3) = 0
x + 4 = 0 x + 3 = 0
x = -4 x = -3
Graphing, Factoring and Solving
Solving goes into graphing as it helps to find certain points on a graph (e.g. x-intercepts, vertex, etc.).