# How do you sketch the graph of #y=-4(x-3)^2+2# and describe the transformation?

##### 1 Answer

See answer below.

#### Explanation:

If you are studying transformations and want to understand how to easily see all the effects for any function, I recommend memorising this general function. It's really worthwhile if you have exams on this stuff.

In this case, the parent function is

and it can have up to four transformations applied to it to get

Now, lets find the four parameters and describe the transformations from the parent function.

The parent function is dilated by a factor of 4 from the x-axis and reflected in the x-axis.

There is no dilation effect from the y-axis.

The function is shifted 3 units to the right.

The function is shifted 2 units up.

To graph, notice that the function is already in turning point form so you can read it straight off as

y-intercept (set

x-intercepts (set

graph{-4(x-3)^2+2 [-10, 10, -5, 5]}