Question

Draw the graph
graph of polynomial p(x) = x² -7x+12
and find it's
Zeroes from the graph
​

Answer 1

Let y = f(x) or, y = 3 - 2x - x2. Let us list a few values of y = 3 - 2x - x2 corresponding to a few values of x as follows : x -5 -4 -3 -2 -1 0 1 2 3 4 y=3-2x-x2 -12 -5 0 3 4 3 0 -5 -12 -21 Thus, the following points lie on the graph of the polynomial y = 2 - 2x - x2: (-5, -12), (-4, -5), (-3, 0), (-2, 4), (-1, 4), (0, 3), (1, 0), (2, - 5), (3, -12) and (4, - 21). Let plot these points on a graph paper and draw a smooth free hand curve passing through these points to obtain the graphs of y = 3 - 2x - x2. The curve thus obtained represents a parabola, as shown in figure. The highest point P(-1, 4), is called a maximum points, is the vertex of the parabola. Vertical line through P is the axis of the parabola. Clearly, parabola is symmetric about the axis.