Exercise 86 Page 40

To graph the function y=2sqrt(x-1)+3, we can create a table of values. We want choose points that will give us an integer. To do that, let's write down the perfect squares and see for what x do we get them.

Perfect Square	x-1	x
0	x-1= 0	1
1	x-1= 1	2
4	x-1= 4	5
9	x-1= 9	10

Now that we have some x-values that will give us an integer square root, we can create a table of values.

x	2sqrt(x-1)+3	Simplify	y
1	2sqrt(1-1)+3	2sqrt(0)+3	3
2	2sqrt(2-1)+3	2sqrt(1)+3	5
5	2sqrt(5-1)+3	2sqrt(4)+3	7
10	2sqrt(10-1)+3	2sqrt(3)+3	9

We will graph the function by plotting the ( x, y) points from the table.

To describe the graph above, we can use the description guidelines from the previous exercise.

Shape: The shape of the graph is a half of a parabola.
Rate of change: As x-value increases y-value also increases, however the rate of change is not constant.
Symmetry: The graph does not look symmetrical.
Possible x- and y-values: The x-values are all numbers greater than or equal to 1, and the y-values are all numbers greater than or equal to 3.
Starting/stopping point: The starting point is (1,3), and there is no stopping point.
Minimum/Maximum: The minimum point is (1,3).