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

##### 1 Answer

Jan 31, 2018

Let's work backwards. First we need to identify the parent function:

graph{y=x^2}

Let's shift the graph to the **right #3# units**

graph{y=(x-3)^2}

Now **up #4# units**

graph{y=(x-3)^2+4}

Now we can **stretch this by a factor of #2#**

graph{y=2(x-3)^2+4}

Our last step is to **flip the graph across the #x#-axis**

graph{y=-2(x-3)^2+4}

Does this graph look the same as the equation we were given?

graph{y=-2(x-3)^2+4}

Yep, so we shifted the parent function