Graph y=0.5x^2+2 find the domain and range

Question

please help

Answer 1

Tierney,

 

As you may know, the graph of this equation is a parabola. The best way to graph this quickly is to plot five points on the graph, including the vertex, and then draw the curve through them.

 

I recommend making a table of values for x and y, then using them to plot the five points.

 

Since the coefficient of x² is a POSITIVE 0.5, the graph will open upward and be wider than the basic shape of y = x².

 

You can choose whatever values for x you like, but integer values usually work best. A good choice would be x = -2, -1, 0, 1, 2. Find the y-values from the equation, then plot the points.

 

Unfortunately, I cannot draw the graph for you in this chat box, but you must learn how to do this yourself on paper. Let me know if you need further help.

Answer 2

The equation given is for a parabola, y = a (x - h)^2 + k with vertex (h,k). The given equation in vertex form would be y = 0.5 (x - 0)^2 + 2 with a vertex at (0, 2).  Because the "a" value in this equation is positive the parabola opens upward from the vertex (0, 2) so the Domain for the equation is (-infinity, 0] u [0, +infinity) or all real numbers and the range is [2, +infinity).