# How do you graph # y=-2(x-2)^2-4#?

##### 1 Answer

Graph:

graph{-2(x-2)^2-4 [-6.54, 13.46, -12.2, -2.2]}

See explanation below.

#### Explanation:

There are more rigorous ways to draw the graph of an parabola by hand (using calculus, mostly), but for our purposes, here's what we're going to do:

**Step 1: Identify the Vertex**

This is just because you have your parabola in vertex form, which makes this process very easy. For a parabola in vertex form

**Step 2: Identify Intercepts**

This is

Now we can stop right there, as we can see that we're gonna end up with the square root of a negative number. Hence, we have *no real #x#-intercepts*.

**Step 3: Identify The Direction of the Parabola**

This is pretty straightforward -- this basically depends on the sign of the *downward*.

**Step 4: Easy Points**

This just means you plug in some values of

Now, you just put everything together, and see what turns out:

graph{-2(x-2)^2-4 [-6.54, 13.46, -12.2, -2.2]}

Does that have everything we just calculated?

Hope that helped :)