Michigan Algebra I Sept. 2012

When graphing a polynomial, the number of different real roots is the number of times the polynomial crosses the x-axis. A root is the place where the polynomial meets the x-axis. At the x-axis, the value of y is always zero. Other names for roots are solutions, x-intercepts, and zeros.

Starting with a polynomial of degree 1, this is a straight line that will cross the x-axis 1 time. The sign of the coefficient of x tells us if the line will be rising or falling as it runs from left to right. When a polynomial is of degree 2, its graph forms a parabola. The coefficient of the x² term now determines if the parabola will open up or down. These functions have been discussed in earlier units.

The next one is a third degree polynomial. Again, the leading coefficient, which in this case is the x³ term, determines which way the graph will point. If it is positive, then the graph will go from the lower left corner to the upper right corner of the grid, while a negative coefficient will give a graph going from the upper left corner to the lower right corner of the grid.