Translating Parabolas

If the parabola @@y = x^2@@ is translated 1 unit down and 4 units to the left, what is the new equation?

• @@y = (x + 4)^2 - 1@@

• @@y = (x - 4)^2 + 1@@

• @@y = (x + 1)^2 - 4@@

• @@y = (x - 1)^2 + 4@@

What is the general form of a parabola's parent equation?

• @@y=x^2@@

• @@y=x^3@@

• @@y=rac{1}{2}x^2@@

• @@y=x+1@@

What is the effect of translating a parabola 3 units to the right?

• The equation changes from @@y = x^2@@ to @@y = (x - 3)^2@@.

• The equation changes from @@y = x^2@@ to @@y = (x + 3)^2@@.

• The equation changes from @@y = x^2@@ to @@y = (x^2 - 3)@@.

• The equation changes from @@y = x^2@@ to @@y = (x + 3)^2 - 3.

If a parabola is translated 2 units up, how does the equation change?

• @@y = x^2 + 2@@

• @@y = x^2 - 2@@

• @@y = x^2 + 1@@

• @@y = x^2 + 3@@

• The parabola opens upwards and creates a minimum.

• The parabola opens downwards and creates a maximum.

• The parabola remains unchanged.

• The parabola opens sideways.

If the parabola @@y = (x + 4)^2@@ is translated 3 units down, what is the new equation?

• @@y = (x + 4)^2 - 3@@

• @@y = (x + 4)^2 + 3@@

• @@y = (x - 4)^2 - 3@@

• @@y = (x + 4)^2 - 5@@

What is the equation of the parabola @@y = x^2@@ translated 4 units down?

• @@y = x^2 - 4@@

• @@y = x^2 + 4@@

• @@y = x^2 - 2@@

• @@y = x^2 + 2@@

What does translating a parabola to the left mean in terms of its equation?

• To translate a parabola to the left, you replace @@x@@ with @@(x+h)@@ where @@h@@ is the number of units moved left.

• To translate a parabola to the left, you replace @@x@@ with @@(x-h)@@ where @@h@@ is the number of units moved left.

• To translate a parabola to the left, you replace @@x@@ with @@(x+2h)@@ where @@h@@ is the number of units moved left.

• To translate a parabola to the left, you replace @@x@@ with @@(x-2h)@@ where @@h@@ is the number of units moved left.