# 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]}