Heather is going to graph y = - 3x^2 + 3. How is the parent graph transformed?

A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

B) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

C) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted left 3 units.

D) The parent graph is reflected over the x-axis, has a vertical compression by a factor of 3 and is shifted up 3 units.

For this case the parent function is given by:

y = x ^ 2

We apply the following transformations:

Reflections:

To graph y = - f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection).

We have then:

y = - x ^ 2

Expansions and vertical compressions:

To graph y = a * f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

We have then:

y = - 3x ^ 2

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

We have then:

y = - 3x ^ 2 + 3

Answer:

A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.