Question

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Answer 1

(a) 5 units up

(b) 3 units right

(c) 7 units left

Explanation:

Parent equation:
`y=x^2`

Transformed equation:
`y = (x - h)^2+ k`

h translates the parabola horizontally

If h > 0 then the translation is h units to the right.

If h < 0 then the translation is h units to the left.

If h = 0 then there is no horizontal translation.

k translates the parabola vertically

If k > 0 then the translation is k units up.

If k < 0 then the translation is k units down.

If k = 0 then there is no vertical translation.

Part (a)

Given equation:
`y=x^2+5`

Rewriting in transformed equation form:
`y=(x-0)^2+5`

Therefore, the parabola is translated 5 units up.

Part (b)

Given equation:
`y=(x-3)^2`

Rewriting in transformed equation form:
`y=(x-3)^2+0`

Therefore, the parabola is translated 3 units right.

Part (c)

Given equation:
`y=(x+7)^2`

Rewriting in transformed equation form:
`y=(x+7)^2+0`

Therefore, the parabola is translated 7 units left.

Part (d)

Given equation: unreadable