(a)        Copy and complete the following table of values for y = 6 + x – 2x²

(b)        Using a scale of 2 cm to 1 unit on the x-axis and a scale of 2 cm to 5 units on the y-axis, draw the graph of the relation
y – 6 + x – 2x² for –3≤ x ≤ 3.
           
(c )       Use your graph to:

(i) find the greatest value of y;
(ii) solve the equation 2x² – x – 11 = 0;
(iii) find the range of values of x for which 6 + x – 2x² ≥ 4.

observation

This question on graph was very popular and well attempted by most candidates.  They were able to complete the table of values and plot the points.  However, the inability of the candidates to read from their graphs was very evident.  They were unable to draw the suitable straight line to solve the equation
2x²– x – 11 = 0 >> 0 = 11 + x – 2x2  >>  - 5 = 6 + x – 2x².  Thus, the straight line that was required was y = -5 and the points of intersection of this line with the graph gives the solution of the equation 2x²– x – 11 = 0.

Candidates were also not able to define the range of values of x for which
6 + x – 2x² ≥ 4.  They were expected to draw the line y = 4 and the solution is those value of x whose corresponding values of y on the graph lie above the line
y = 4.