Question

Draw the graph of the polynomial f(x) = x2

-2x-8 and find zeroes. Verify the
zeroes of the polynomial.​

Answer 1

Let y = x2

-2x-8

The following table given the values of y for various values of x.

The Points (-3, 7), (-2, 0), (-1, -5), (0, -8), (1, -9), (2, -8), (3, -5), (4, 0) and (5, 7) are plotted

on the graph paper on the suitable scale and drawn a smooth free hand curve passing through

these points.

The curve thus obtained represents the graph of the polynomial y = x2

-2x-8. This is called a parabola.

The curve cuts the x – axis at (-2, 0) and (4, 0) .

The x – coordinates of these points are zeroes of the polynomial y = x2

-2x-8. Thus -2 and 4

are the zeroes.

Verification:

To find zeroes of x2-2x-8

x2-2x-8 ⇒ x2-4x+2x-8 = 0

x(x-4)+2(x-4) = 0

(x-4) (x+2) = 0

x – 4 = 0 or x+2 =0 ⇒ x = 4 or -2 are the zeroes.