Pre Calculus 11 Notes

By: Gen L.

In partnership with Hyperion University, 2023

Lesson 3: Writing Equations

Terms:

  • Translation: Moving the vertex in space
  • Vertical Compression / Expansion: Vertically stretching in relation to parent function.

Transforming Functions

  • Using vertex form, the graphs are translated as indicated:
Variables Reflect Vertical Translate
a a*-1 a -
p - - Horizontal
q - - Vertical

Example no. 1

  • Translation of 10 units down:
a 1
p 0
q -10
  • Function:

Example no. 2

  • Translation of 4 units right:
a 1
p 4
q 0
  • Function:

Example no. 3

  • A vertical expansion of 6, reflected in the x-axis
    • Reflected means the value is inverted.
a -6
p 0
q 0
  • Function:

Example no. 4

  • A vertical expansion of 4, a translation of 6 units left and 5 units up.
a 4
p -6
q 5
  • Function:

Vertex / Point Form

  • Example: A vertex of and passes through the point .

  • We know & , what about ?

    • Solve for

  • Remember this equation? , we can use this to solve for . Just plug in the values.

Example:

  1. Determine your table:
a p q x y
a 2 -3 4 5
  1. Plug in values:

Example, cont:

  1. Solve for :

, Start with parenthesis.
, then exponents.
, then isolate any terms.
, and divide.

  1. Update your table:
a p q x y
2 2 -3 4 5

Example, cont:

a 2
p 2
q -3
  • Function:

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