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
 
 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.