Question

PLSSS HELP ME WITH THESE :)))

Answer 1

7)
`x \to x - 3`.

8)
`y \to y + 2`

9) The entire quadratic equation did not get reflected.

Explanation:

7) A horizontal translation to the right is of the form:

`x \to x - a`

Let
`y = -(x-3)^(2) + 2`, then the horizontal translation is represented by
`x \to x - 3`.

8) A vertical translation upwards is of the form:

`y \to y + a`

Let
`y = -(x-3)^(2) + 2` , then the vertical translation is represented by:

`y \to y + 2`

9) The only component of the quadratic equation that was reflected was the part
`(x-3) ^(2)` along the x-axis. We can create the entire function by applying the following steps:

(i)
`f(x) = x^(2)` (Original function)

(ii)
`f(x) = (x-3)^(2)` (Horizontal translation)

(iii)
`f(x) = - (x-3)^(2)` (Reflection)

(iv)
`f(x) = -(x-3)^(2) + 2` (Vertical translation)

The entire quadratic equation did not get reflected.