Question

8(a). Copy and complete the table of values for y=2x²-x-4 for -3≤x≤3.
8(b). Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of y=2x²-x-4 for -3≤x≤3.
8(c). Use the graph to find the: (i) roots of the equation 2x²-x-4=0; (ii) values of x for which y increases as x increases; (iii) minimum point of y.

Accepted Answer

(a) Completed table: x: -3,-2,-1,0,1,2,3 → y: 17,10,-1,-4,-3,2,11 (computed using y=2x²-x-4 for each x value).
(b) Plotting these points on the given scale produces a parabola (U-shaped curve) with a minimum point.
(c)(i) From the graph, the roots of the equation are the values of x where the graph cuts the x-axis, approximately x=-1.2 and x=1.7.
(ii) The values of x for which y increases as x increases is the right-hand side of the curve, approximately 0.1≤x≤3.
(iii) The minimum point of y is y=-4 (occurring around x=0.25 based on the curve's vertex).

WAEC Mathematics 2023 Theory — Question 8

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