Pre-Calculus 11 Notes

By: Gen L.

Lesson 1: Intro to Quadratic Functions

Standard Form

• Standard form of a quadratic function:
  Or
• Important:
  • Degree always exactly 2
  • Sometimes the is not present ()

Putting Numbers to It: a,b,c

• • affects the width & direction of the function
    ()
• • affects the vertex location (min/max,Axis)
• • affects the -intercept (function crosses y-axis)

Vertex Form

• Vertex form of a quadratic function:
  
• Note: 's value is inverted

Putting Numbers to It: a,p,q

• • affects the width & direction of the function
    ()
• • affects the -coordinate of the vertex
• • affects the -coordinate of the vertex

Characteristics

1. Direction
   • Based on value

   Value	+	-
   Direction	Up	Down

2. Width
   • If , is narrower,
   • If , is normal,
   • If , is wider.

Characteristics

3. Axis of Symmetry (AoS)
   • The vertical line through the vertex ()
4. Vertex
   • The min/max point of the function ( in vertex form)
5. Intercepts
   • Y-intercept
     • Where the function crosses y-axis ( in standard form)

Characteristics

5. Intercepts, cont.
   • X-intercept
     • Where the function crosses x-axis
6. Min/Max
   • Highest/Lowest point of function (-coordinate of vertex, based on direction)
7. Domain
   • Possible values of function ()
8. Range
   • Possible values of function ( max or min)

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