a zero of a quadratic polynomial. Consider the quadratic polynomial x – x – . Let us see what the graph * of y = x – x – looks like. Let us list a few values of y = x – x – corresponding to a few values for x as given in Table .
. * Plotting of graphs of quadratic or cubic polynomials is not meant to be done by the students, nor is to be evaluated. Fig. .
Table . – – y = x – x – – – – – If we locate the points listed above on a graph paper and draw the graph, it will actually look like the one given in Fig. . .
In fact, for any quadratic polynomial ax + bx + c , a , the graph of the corresponding equation y = ax + bx + c has one of the two shapes either open upwards like or open downwards like depending on whether a > or a < . (These curves are called parabolas .) You can see from Table . that – and are zeroes of the quadratic polynomial. Also note from Fig.
. that – and are the x -coordinates of the points where the graph of y = x – x – intersects the x -axis. Thus, the zeroes of the quadratic polynomial x – x – are x -coordinates of the points where the graph of y = x – x – intersects the x -axis. This fact is true for any quadratic polynomial, i.e., the zeroes of a quadratic polynomial ax + bx + c , a , are precisely the x -coordinates of the points where the parabola representing y = ax + bx + c intersects the x -axis.
From our observation earlier about the shape of the graph of y = ax