How do you graph the function y=1/2x^2+2x-3/8 and identify the domain and range?

1 Answer
Feb 11, 2018

Domain: (-oo, oo)
Range: (1/2, oo)

Explanation:

How to graph the function:

1) Find the zeros or roots of the function

This can be done by factoring the quadratic equation.

In this case your zeros are: -2+-sqrt(4.75).

This can be found using the quadratic formula: (-b+-sqrt(b^2-4ac))/(2a). Where a, b, and c are the coefficients of the terms in your quadratic equation.

2) Find the vertex

This can be done by rewriting your quadratic equation into vertex form: y = a*(x-h)^2 + k
Where h and k are the x and y coordinates of the vertex.

3) You can insert more values into x and calculate the y coordinate. This step is optional because you should be able to draw the parabola with the 3 points already discovered.

How to identify the domain and range

1) Domain

The domain of any quadratic is always (-oo, oo) this is because no matter what x value you choose from -oo to oo there is always a y.

2) Range

The range of any quadratic is from the vertex either all values below or above.

To know whether the parabola faces up like a U or down like an upside down U you look for the sign of the leading coefficient, or a. In this case the leading coefficient is 1/2, a positive number. Therefore in this case the range consists of the vertex point and all values above it. So the range is (1/2, oo)