Pre-Calculus Desmos File Library

  • Table of Points 
  • Conic Sections 
    • Parabolas
    • Circles
    • Ellipses
    • Hyperbolas
  • Piecewise Functions
    • Step Functions
  • Absolute Value Functions
Tables of Points

Conic Sections
Standard Form Conic Equations

Parabolas (Vertex Form)

Quadratic Functions (Vertex Form)

This slider based document is the basis for all of the quadratic function's seen in this section​
Parabolas 101: Opens Up or Down FUNCTIONS
  • DESMOS File
  • this file will show 
    • axis of symmetry
    • focus
    • directrix line
    • x intercepts
    • y intercept
    • a, h, and k are integers
    • lines that help support the definition of a parabola
    • points with particular integer x values
    • points with particular integer y values
A > 0 Opens UP
0 < A < 1 Vertical Compression
vertex (h,k) any integer in [-10,10]
A > 1 Vertical Stretch
​vertex (h,k) any integer in [-10,10]
Parabolas 101: Opens Up or Down FUNCTIONS
Parabolas 101: Opens Down FUNCTIONS
  • DESMOS File
  •  A < -1
  • this is a vertical stretch
  • this is a vertical reflection 
Parabolas 101: Opens Down FUNCTIONS
  • DESMOS File
  • A < -1
  • this is a vertical stretch
  • this is a vertical reflection 
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Down FUNCTIONS
  • DESMOS File
  •  A < -1
  • this is a vertical stretch
  • this is a vertical reflection 
  • k = 0
  • vertex on x axis
Parabolas 101: Opens Down FUNCTIONS
  • DESMOS File
  •  -1 < A < 0
  • this is a vertical compression 
  • this is a vertical reflection
Parabolas 101: Opens Down FUNCTIONS
  • DESMOS File
  •  -1 < A < 0
  • this is a vertical compression 
  • this is a vertical reflection
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Down FUNCTIONS
  • DESMOS File
  •  -1 < A < 0
  • this is a vertical compression 
  • this is a vertical reflection
  • k = 0
  • vertex on x axis
Parabolas 101: Opens Up FUNCTIONS
Parabolas 101: Opens Up FUNCTIONS
  • DESMOS File
  •  0 < A < 1
  • this is a vertical compression
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Up FUNCTIONS
  • DESMOS File
  •  0 < A < 1
  • this is a vertical compression
  • k = 0
  • vertex on x axis
Parabolas 101: Opens Up FUNCTIONS
Parabolas 101: Opens Up FUNCTIONS
  • DESMOS File
  •  A > 1
  • this is a vertical stretch 
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Up FUNCTIONS
  • DESMOS File
  •  A > 1
  • this is a vertical stretch 
  • k = 0
  • vertex on x axis

Quadratic Relations (Vertex Form)

Parabolas 101: Opens Left and Right RELATIONS ONLY
Parabolas 101: Opens Left RELATIONS ONLY
Parabolas 101: Opens Right RELATIONS ONLY
Parabolas 101: Opens Left and Right RELATIONS ONLY
Parabolas 101: Opens Left and Right RELATIONS ONLY
Parabolas 101: Opens Left and Right RELATIONS ONLY
Parabolas 101: Opens Left RELATIONS ONLY
  • ​DESMOS File
  • A < -1
  • this is a horizontal stretch
  • this is a horizontal reflection
Parabolas 101: Opens Left RELATIONS ONLY
  • ​DESMOS File
  • A < -1
  • this is a horizontal stretch
  • this is a horizontal reflection
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Left RELATIONS ONLY
  • ​DESMOS File
  • A < -1
  • this is a horizontal stretch
  • this is a horizontal reflection
  • k = 0
  • vertex on x axis
Parabolas 101: Opens Left RELATIONS ONLY
  • ​DESMOS File
  •  -1 < A < 0
  • this is a horizontal compression
  • this is a horizontal reflection
Parabolas 101: Opens Left RELATIONS ONLY
  • ​DESMOS File
  •  -1 < A < 0
  • this is a horizontal compression
  • this is a horizontal reflection
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Left RELATIONS ONLY
  • ​DESMOS File
  •  -1 < A < 0
  • this is a horizontal compression
  • this is a horizontal reflection
  • k = 0
  • vertex on x axis
Parabolas 101: Opens Right RELATIONS ONLY
  • ​DESMOS File
  •  0 < A < 1
  • this is a horizontal compression 
Parabolas 101: Opens Right RELATIONS ONLY
  • ​DESMOS File
  •  0 < A < 1
  • this is a horizontal compression
  • h = 0
  • vertex on y axis
Parabolas 101: Opens Right RELATIONS ONLY
  • ​DESMOS File
  •  0 < A < 1
  • this is a horizontal compression
  • k = 0
  • vertex on x axis
Parabolas 101: Opens Right RELATIONS ONLY
Parabolas 101: Opens Right RELATIONS ONLY
Parabolas 101: Opens Right RELATIONS ONLY
  • ​DESMOS File
  • A > 1
  • this is a horizontal stretch
  • k = 0
  • vertex on x axis

General Form Conic Equations

General Conic Equation 101: integer coefficients and constants
General Conic Equation 101: integer coefficients and constants

Parabolas

Parabolas 101:General Form (opens UP and DOWN)
  • ​DESMOS File
  • this file has no XY term
  • this file has no Y squared term
Parabolas 101:General Form (opens LEFT and RIGHT)
  • ​DESMOS File
  • this file has no XY term
  • this file has no X squared term

Circles

Circle 101:General Form 
Circle 101:General Form no x or y term
  • ​DESMOS File
  • this file has no X term
  • this file has no Y term
Circle 101:General Form no x term
Circle 101:General Form no y term

Ellipses

Ellipse 101:General Form 
  • ​DESMOS File
  • this file has no XY term
  • A and B > 0 
  • When A = B circle is present
Ellipse 101:General Form C = 0
  • ​DESMOS File
  • this file has no XY term
  • A and B > 0 
  • When A = B circle is present
  • C = 0
Ellipse 101:General Form D = 0
  • ​DESMOS File
  • this file has no XY term
  • A and B > 0 
  • When A = B circle is present
  • D = 0
Ellipse 101:General Form C & D = 0
  • ​DESMOS File
  • this file has no XY term
  • A and B > 0 
  • When A = B circle is present
  • C = 0
  • D = 0
Ellipse 101:General Form C = 0
  • ​DESMOS File
  • this file has no XY term
  • A and B < 0 
  • When A = B circle is present
  • C = 0
Ellipse 101:General Form D = 0
  • ​DESMOS File
  • this file has no XY term
  • A and B < 0 
  • When A = B circle is present
  • D = 0
Ellipse 101:General Form C & D = 0
  • ​DESMOS File
  • this file has no XY term
  • A and B < 0 
  • When A = B circle is present
  • C = 0
  • D = 0
Ellipse 101:General Form 
Ellipse 101:General Form D = 0
Ellipse 101:General Form E = 0
  • ​DESMOS File
  • this file has an XY term
  • A and B > 0 
  • E = 0
Ellipse 101:General Form D & E = 0
  • ​DESMOS File
  • this file has an XY term
  • A and B > 0 
  • D = 0
  • E = 0
Ellipse 101:General Form D = 0
Ellipse 101:General Form E = 0
  • ​DESMOS File
  • this file has an XY term
  • A and B < 0 
  • E = 0
Ellipse 101:General Form D & E = 0
  • ​DESMOS File
  • this file has an XY term
  • A and B < 0 
  • D = 0
  • E = 0

Hyperbolas

Hyperbola 101:General Form 
  • ​DESMOS File
  • this file has no XY term
  • A > 0 and B < 0 
Hyperbola101:General Form C = 0
  • ​DESMOS File
  • this file has no XY term
  • A > 0 and B < 0 
  • C = 0
Hyperbola101:General Form D = 0
Hyperbola101:General Form C = 0 & D = 0
  • ​DESMOS File
  • this file has no XY term
  • A > 0 and B < 0 
  • C = 0
  • D = 0
Hyperbola 101:General Form 
  • ​DESMOS File
  • this file has no XY term
  • A < 0 and B > 0 
Hyperbola101:General Form C = 0
Hyperbola101:General Form D = 0
  • ​DESMOS File
  • this file has no XY term
  • A < 0 and B > 0 
  • D = 0
Hyperbola101:General Form C = 0 & D = 0
  • ​DESMOS File
  • this file has no XY term
  • A < 0 and B > 0 
  • C = 0
  • D = 0
Hyperbola 101:General Form 
  • ​DESMOS File
  • this file has an XY term
  • A > 0 and B < 0 
Hyperbola101:General Form D = 0
  • ​DESMOS File
  • this file has an XY term
  • A > 0 and B < 0 
  • D = 0
Hyperbola101:General Form E = 0
Hyperbola101:General Form C = 0 & D = 0
  • ​DESMOS File
  • this file has an XY term
  • A > 0 and B < 0 
  • C = 0
  • D = 0
Hyperbola 101:General Form 
  • ​DESMOS File
  • this file has an XY term
  • A < 0 and B > 0 
Hyperbola101:General Form D = 0
Hyperbola101:General Form E = 0
  • ​DESMOS File
  • this file has an XY term
  • A < 0 and B > 0 
  • E = 0
Hyperbola101:General Form D = 0 & E = 0
  • ​DESMOS File
  • this file has an XY term
  • A < 0 and B > 0 
  • D = 0
  • E = 0

Piecewise Functions

  • these files will allow you to plot a piecewise function with up to six pieces 
  • these files will allow you to toggle the type of endpoints each constraint has
  • these files will allow you to see integer x coordinates within the constraints
  • these files will allow you to show behavior as x approaches boundary values from the left or right 
Piecewise 101: 1 piece function
Piecewise 101: 4 piece function
Piecewise 101: 2 piece function
Piecewise 101: 5 piece function
Piecewise 101: 3 piece function
Piecewise 101: 6 piece function

Step Functions

Step Functions 101: Ceiling Function
  • DESMOS File
  • this is also called the greatest integer function 
  • notice the types of endpoints 
Step Functions 101: Floor Function
  • DESMOS File
  • this is also called the least integer function 
  • notice the types of endpoints 

Absolute Value Functions

Absolute Value Function 101: Parent Absolute Value Function and its reflection
Absolute Value Function 101: All A transformations of Parent Absolute Value Function
  • DESMOS File
  • dynamically shows all of the different types of A transformation
  • A transformations 
    • A < -1 Vertical Stretch and Vertical Reflection
    • A = -1 Vertical Reflection
    • -1 < A < 0 Vertical Compression and Vertical Reflection
    • 0 < A < 1 Vertical Compression
    • A = 1 Parent Function
    • A > 1 Vertical Stretch
Absolute Value Function 101: All Negative A transformations of Parent Absolute Value Function
  • DESMOS File
  • dynamically shows all of the NEGATIVE A types of A transformation
  • A transformations 
    • A < -1 Vertical Stretch and Vertical Reflection
    • A = -1 Vertical Reflection
    • -1 < A < 0 Vertical Compression and Vertical Reflection
Absolute Value Function 101: All A transformations of Parent Absolute Value Function
  • DESMOS File
  • dynamically shows all of the different types of A transformation
  • A transformations 
    • A < -1 Vertical Stretch and Vertical Reflection
    • A = -1 Vertical Reflection
    • -1 < A < 0 Vertical Compression and Vertical Reflection
    • 0 < A < 1 Vertical Compression
    • A = 1 Parent Function
    • A > 1 Vertical Stretch
Absolute Value Function 101: All A transformations of Parent Absolute Value Function
  • DESMOS File
  • dynamically shows all of the different types of A transformation
  • A transformations 
    • A < -1 Vertical Stretch and Vertical Reflection
    • A = -1 Vertical Reflection
    • -1 < A < 0 Vertical Compression and Vertical Reflection
    • 0 < A < 1 Vertical Compression
    • A = 1 Parent Function
    • A > 1 Vertical Stretch

Polar Coordinate System

Continuous Functions

Not Continuous Functions

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