J17

Example
Draw the graphs of y = x 2 and y = -x 2 for values of x between -2 and +2.
Solution
Graph of y = x 2 :
Make a table of values for (x, y)
x -5 -4 -3 -2 -1 0 1 2 3 4 5
y 25 16 9 4 1 0 1 4 9 16 25
Plot these points on a graph paper and label the axes x, y. Since the values of y are all
positive, x-axis should be drawn near the bottom of the paper.
As the values of x are between -2 and +2, y-axis should be taken in the middle of the
paper. The scale chosen must be convenient but not necessarily the same o both axes.
The resulting diagram should cover an area which is more than half the page on which it
is drawn (but the whole diagram should fit on the same page).
Note:
(a) The minimum value of the curve is 0 at the origin, i.e. the curve turns at the origin
(b) The curve is symmetrical about the y – axis.
The graph of y = -x 2
All values of y are numerically the same as the corresponding values of y in
y = x 2 but are negative. The shape of the curve will be the same but inverted.