# How do you graph the function #0 = x^2+6x+9# ?

##### 2 Answers

See explanation...

#### Explanation:

The given expression:

#0 = x^2+6x+9#

is an equation, not a function.

We can express the related function as:

#f(x) = x^2+6x+9 = (x+3)^2#

In which case the given equation represents the zeros of the function, i.e. the intersections of

Note that for any real number

Hence:

#(x+3)^2 >= 0#

with equality if and only if

So what we have here is a parabola with vertex on the

To find the intersection with the

#f(0) = 0^2+6(0)+9 = 9#

That is:

We could evaluate

graph{x^2+6x+9 [-8, 3, -1.1, 10.2]}

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

#### Explanation:

This is in the form

We know

I.e.