How would I graph x²+6x+6? And what does -6≤x≤0 mean?

You graph the equation by plotting the points {(x,y) ∈ ℝ² | y=x²+6x+6}.

The second thing is the set {x ∈ ℝ| -6≤x≤0}

y = x² + 6x + 6

When x = 0, y = 6. Y intercept is (0, 6). To find where graph cuts x-axis put y = 0.

x² + 6x + 6 = 0

Completing the square (x + 3)² - 3 = 0

x + 3 = ±√3

x = -3 - √3 and x = -3 + √3. Graph cuts x-axis at (-3 - √3, 0) and

(-3 + √3, 0). As you probably know this is the graph of an upwards opening parabola.

-6≤x≤0 simply means that x can take any value between -6 and 0 where -6 and 0 are included.

You'd plot x²+6x+6 by setting that equal to y (y = x²+6x+6), and then finding the value of why for certain values of x. The -6≤x≤0 defines the range of your function. This means that the plot is only going to run from -6 to 0 (including both -6 and 0), you're not going to consider any other points outside of what's been given.

Set this function equal to y and plug in some points. Then plot and graph those points.

-6≤x≤0 means that any value of x must be greater than or equal to -6, and smaller than or equal to 0

:)