Translating Parabolas

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

• y=(x-2)²+3
• y=(x-2)²-3
• y=(x+2)²+3
• y=(x+2)²-3

Tags

CCSS.HSF-IF.C.7A

How would you describe the translation from f(x)=x²  to  f(x)=(x-3)² ?

• Horizontal translation: three units to the left

• Horizontal translation: three units to the right

• Vertical translation: three units up

• Vertical translation: three units down

How would you describe the translation from f(x)=x²  to  f(x)=x²+5 ?

• Horizontal translation: five units to the right

• Horizontal translation: five units to the left

• Vertical translation: five units up

• Vertical translation: five units down

Given a parabola with a vertex at (4,3) and a directrix of y=1, write the equation of the parabola.

Mathematical Equivalence

ON

Given a parabola with a vertex of (4,0) and a focus of (4,-1) write the equation of the parabola.

Mathematical Equivalence

ON

• y=(x-1)²+5
• y=(x-1)²-5
• y=(x+1)²+5
• y=(x+1)²-5

Tags

CCSS.HSF-IF.C.7A

• y=(x-5)²+2
• y=(x-5)²-2
• y=(x+5)²+2
• y=(x+5)²-2

Tags

CCSS.HSF-IF.C.7A

How would you describe the translation from    f(x)=(x-2)² to  f(x)=(x+3)² ?

• Horizontal translation: to the right 3 units

• Horizontal translation: to the left 2 units

• Horizontal translation: to the left 5 units

• Horizontal translation: to the right 5 units

Describe the translation from f(x)=(x+2)²-3  to  f(x)=(x-3)²-5

• Five units to the right, 2 units up

• Five units to the right, 2 units down

• Five units to the left, 2 units up

• Five units to the left, 2 units down