(a) Figure 1(c) in the text shows a graph of the equation y = x2 + 3x -5. Use a grap...

(a) Figure 1(c) in the text shows a graph of the equation y = x² + 3x -5. Use a graphing utility to reproduce the graph. [Use the same viewing rectangle that is used in Figure 1(c).]

(b) Add the graph of the equation y = x² - 3x - 5 to the picture that you obtained in part (a). (This new equation is the same as the one in part (a) except that the sign of the coefficient of x has been reversed.) Note that the x-intercepts of the two graphs appear to be negatives of one another.

(c) Use the quadratic formula to determine exact expressions for the roots of the two equations x² - 3x - 5 = 0 and x² - 3x - 5 = 0. You’ll find that the roots of one equation are the opposites of the roots of the other equation. [In general, the graphs of the two equations y = ax² + bx + c and y = ax² - bx + c are symmetric about the y-axis. Thus, the x-intercepts (when they exist) will always be opposites of one another.]