Expert: Chanda Walker - 3/2/2009

Question
Hi, how you doing. It's me again looking for more math help lol. We started a new unit and I'm having a hard time solving these 2 questions.

Write the coordinates of the image of the point (-3,9) on the graph y=x^2 when each of the following transformations are applied.

a) Y= -x^2+4 (reflection in the x-axis, followed by a vertical translation of 4 units up)
b) Y=1/3x^2 (Vertical compression of 1/3)

The Y2 coordinates are -5 and 3 respectively. Would that be the answer?

(-3,-5) and (-3,3)?

The Quadratic function f(x)=x2 is transformed to f(x)=-1/2(x+3)^2+1
The point of (1, 1) on the graph of y=x2 is transformed to which point on the graph y=-1/2(x+3)^2+1

I graphed it but don't know where else to go from there.

Thanks in advance.

Answer
I'm doing fine.  Thanks for asking!  I'm happy you are back, except of course that you're struggling with new problems.  But we'll fix that. :)

For a) and b) you have those answers correct.

*********************

y = -1/2(x + 3)^2 + 1

I suggest you take each transformation and analyze what they do to the point one step at a time.

The point was first shifted to the left by 3.
y = (x + 3)^2

(-6, 9)

Then the y scale was compressed by 2 and reflected about the x axis.
y = (-1/2)(x+3)^2

(-6, -9/2)

Finally it was shifted up one.
y = -1/2(x + 3)^2 + 1

(-6, -7/2 )