Question

Represent the following quadratic polynomial graphically and there zeroes: <br />- x^2 - 2x + 3 (8 graph points)​

Answer 1

Answer:

Let us draw the graph of y=x

2

−2x−3.

Now, form the following table by assigning integer values from −3 to 4 for x and finding the corresponding values of y=x

2

−2x−3.

x −3 −2 −1 0 1 2 3 4

x

2

9 4 1 0 1 4 9 16

−2x 6 4 2 0 −2 −4 −6 −8

−3 −3 −3 −3 −3 −3 −3 −3 −3

y 12 5 0 −3 −4 −3 0 5

Plot the points (−3,12),(−2,5),(−1,0),(0,−3),(1,−4),(2,−3),(3,0),(4,5) and join the points by a smooth curve.

The curve intersects the x-axis at the points (−1,0) and (3,0)

The x-coordinates of the above points are −1 and 3

Hence, the solution set is {−1,3}.

Note

(i) On the x-axis, y=0 always.

(ii) The values of y are both positive and negative. Thus, the curve lies below and above the x-axis.

(iii) The curve is symmetric about the line x=1. (It is not symmetric about the y-axis)