Transformations of Quadratic Equations

• Maximum

• Left 5

• Down 8

• vertical shrink

• Minimum

• Right 5

• Up 8

• Vertical Stretch

• No Vertical Shift

Shift f(x)=x² three units to the left and 4 units down

• f(x)=(x+3)²-4

• f(x)=(x-3)²-4

• f(x)=(x+4)²-3

• f(x)=(x-4)²-3

• up 3

• down 3

• right 1

• left 1

• across x axis

• upward

If the blue graph is
f(x) = x² 
the red must be...

• g(x) = (x + 3)²

• g(x) = (x - 3)²

• g(x) = x² + 3

• g(x) = x² - 2

• up 3

• down 3

• right 1

• left 1

• downward

• upward

If the blue graph is
f(x) = x² 
then the red must be...

Mathematical Equivalence

ON

• compress

• stretch

• Reflection over the x-axis

• Vertical Shrink by 2

• Vertical Shrink by 0.7

• Vertical Stretch up 2

• compress

• stretch

• (h,k) = (2,-3)

• 
• (h,k) = (-2,3)

• 
• (h,k) = (-3,-2)

•