How do you sketch the graph of #y=-2(x-1)^2+7# and describe the transformation?
1 Answer
See method below.
Explanation:
Transformation
Let
This is a translation by 1 to the right.
This is a vertical stretch, scale factor 2.
This is a reflection in the x-axis (y=0).
This is a translation up by 7.
Put this together; our transformation is:
Reflection in the x-axis, vetical stretch scale factor 2, transformation by
Sketching
We need to find some points to plot the curve.
From this completed square form, we can tell that the minimum will be at
Find the x-intercepts:
Let
so
Find the y-intercepts:
Let
So there is a y-intercept at
The co-efficient of
The graph should look like this:
graph{-2(x-1)^2+7 [-14.16, 17.88, -6.48, 9.54]}