How do you find the domain and range of y=-x^2-3x-3?

1 Answer
Alvin L.
Dec 16, 2017

Domain: x in RR
Range: {y|y<=-3/4}

Explanation:

The function is defined for all real x, so the domain is just the real numbers, RR.

To find the range, we will consider the function as a parabola. Since the x^2 term is negative, we know the parabola will be concave down (nn). Therefor the range will be between -oo and the vertex of the parabola.

The x coordinate of the vertex of a parabola ax^2+bx+c can be found using the following formula:
-b/(2a)

Plugging in our numbers, we get:
(-(-3))/(-2)=-3/2

Now, we want the y coordinate of the vertex, so we plug in the value into the original function:
-(-3/2)^2-3(-3/2)-3=-9/4+9/2-3=-9/4+18/4-12/4

=-3/4

So we know the vertex is at -3/4. This means that the range of the function is {y|y<=-3/4}

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