properties
Graphing Steps
Transformations from Graphs
Transformations from Equations
Equations from Transformations
100
The Domain for any quadratic function
What is (-∞,∞)?
100
What is the first step to graphing a quadratic function?
Determine hands of parabola up or down
100
The transformation from the parent function to the graph on the image below:
What is a horizontal shift left 2 units?
100
The transformation that occurs in the quadratic function
f(x)=x^2+4
What is a vertical shift up 4 units?
100
A quadratic function that has been vertically shifted up 2 units
What is
y=x^2+2
200
The point at which the parabola changes direction
What is the vertex?
200
What is the second step to graphing a quadratic function?
find y-intercept
200
The transformation that occurs from the parent function to the graph below
What is a vertical shift down 3?
200
The transformation that occurs in the quadratic function
f(x)=(x-1)^2
What is a horizontal shift right 1 unit?
200
A quadratic function that has been horizontally shifted left 9 units
What is
y=(x+9)^2
300
Find the Range of the function: y=x2-5
[-5;+oo)
300
How to find the Vertex of a Parabola?
x=-b/2a y=-D/4a
300
The transformations that occur from the parent function to the graph below
What are a horizontal shift right 3 and a vertical shift down 2?
300
The transformation that occurs in the quadratic function
f(x)=3x^2
What is a vertical stretch of 3?
300
A quadratic function that has been horizontally shifted right 1 unit and vertically shifted down 4 units
What is
y=(x-1)^2-4
400
Find the Range of the function: y=(x+3)2+2
[2;+oo)
400
What is the third step to graphing a quadratic function?
find x-intercept (solve quadratic equation)
400
The transformations from the parent function to the graph below
What are a horizontal shift left 5 units and a vertical shift up 1 unit?
400
The Transformations that Occur in the Quadratic Function
f(x)=1/4(x+5)^2-7
What are a vertical compression of 1/4, a horizontal shift left 5, and a vertical shift left down 7?
400
A quadratic function that has been vertically shifted down 3 units, horizontally shifted left 6 units, and reflected over the x-axis
What is
y=-(x+6)^2-3
500
Find the Range of the function: y=-(x+6)2-8
(-oo;-8]
500
what is axis of symmetry of a parabola?
The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric
500
The transformations from the parent function to the graph shown below
What are a reflection over the x-axis, a horizontal shift right 3 units, and a vertical shift up 2 units?
500
The transformations that occur in the quadratic function
f(x)=-2(x-3)^2+4
What are a reflection across the x-axis, a vertical stretch of 2, a horizontal shift right 3 units, and a vertical shift up 4 units?
500
A quadratic function that has been reflected over the x-axis, has been vertically stretched by a factor of 4, and has a vertex at (2,-5)
What is
y=-4(x-2)^2-5