Question

The graph of y=x^2 was transformed to Y= -(x+3)^2 +5. Describe all transformations applied to the original function and determine by how many units if necessary

Answer 1

Hey there!

1. The graph was flipped vertically and now opens downward.

We know this because there is a negative sign in front of the equation:

`y=`
`\boxed-`
`(x+3)^2+5`

2. The graph was moved 3 units to the left.

We know this because there is 3 added to x inside of the parenthesis. Remember, inside (parenthesis) is opposite and acts on x, outside (parenthesis) is same and acts on y.

`y=-(x\boxed{+3})^2+5`

3. The graph was moved 5 units up.

We know this because there is 5 added at the end of the equation. It acts on y because it is outside of the parenthesis.

`y=-(x+3)^2\boxed{+5}`

Hope this helps!