Question

6(a) The graph shows the relation of the form y=mx²+mx+r, where m, n and r are constants. Using the graph: (i) state the scale used on both axes; (ii) find the values of m, n and r; (iii) find the gradient of the line through P and Q; (iv) state the range of values of x for which y>0.

Accepted Answer

(i) Scale: x-axis: 2cm to represent 2 units; y-axis: 2cm to represent 10 units.

(ii) From the graph, the roots of the curve are x=−2 and x=4.
(x+2)=0 and (x−4)=0 ⟹ (x+2)(x−4)=0
x²−4x+2x−8=0
x²−2x−8=0
Since the given curve is a maximum curve, i.e. the coefficient of x² must be negative, multiply through by (−1):
−x²+2x+8=0
Comparing with mx²+nx+r=0: m=−1, n=2, r=8.

(iii) To find the gradient of |PQ|, from the given curve P(−5,−27) and Q(3,5):
Gradient = (y₂−y₁)/(x₂−x₁) = (5−(−27))/(3−(−5)) = 32/8 = 4.

(iv) Range: {x: −2<x<4}.

WAEC Mathematics 2022 Theory — Question 6

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