How do you find the domain and range of y=x^2+3x+1?

1 Answer
Ryuu
May 2, 2017

"D":{x inRR}
"R":{y inRR|y>=-1.25}.

Explanation:

The domain and range are a set of all the possible values that a function can have.

Domain refers to the x-coordinate, and range refers to the y-coordinate.

For a parabola, no matter the values, the domain will always be "D":{x inRR} (unless context is given).

As for range, the range is dependent on the c-value of the equation (only in vertex form).

This is because, if the c-value (again, only in vertex form) is 1, then the parabola is moved up 1 units. Meaning any value below 1 is inadmissible.

Unfortunately, in this case (standard form), the c-value refers to the y-intercept. We can convert the equation to vertex form, or we can graph it and examine the parabola. We'll do that.

graph{x^2 + 3x + 1 [-3.895, 3.9, -1.948, 1.947]}

As you can see, the domain can be any x-value, while the range can only be values equal to or above the vertex's y-coordinate, -1.25.

Therefore, the range is "R":{y inRR|y>=-1.25}.

Hope this helps :)

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