It's odd that you would be asked so many topics that aren't covered at all in your text. Since you haven't been taught this material, you might need lessons for the following instructions to make sense.
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domain: the domain is all allowable input values; generally, the domain is the x-values. (In your specific case, the domain would be the u-values.) So figure out which values on the number line are "okay" to plug in for u.
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range: the range is all the output values; often, the range is determined by looking at the graph; the range is generally the y-values. (In your specific case, the range would be the v-values.) So look at the graph, and figure out which y-values the parabola goes by.
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vertex: the vertex is the point on the parabola where the graph changes direction; either the lowest or the highest point on the parabola. So either
complete the square to find the vertex, or use
the formula. Check your work with a graph.
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x- and y-intercepts: the intercepts are where the graph crosses the x- and y-axes, respectively; to find the y-intercept(s), plug zero in for x and solve; to find the x-intercept(s), plug zero in for y and solve. In your case, plug zero in for u to find the v-intercepts, and then plug zero in for v to find the u-intercepts. (Since you don't have "x" or "y" in your equation, you can't have "x-" or "y-intercepts".)
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direction of opening: positive quadratics open upward; negative quadratics open downward. (If you'd done any work with quadratics in class or whatever, you would have noticed this, but since quadratics aren't covered in your text, you may need to do some graphing of your own "on the side" to learn how this works.) So look at the sign on the leading term, and determine which way the parabola goes. (Or do the graph.)
Eliz.
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