Question

7. (a) Copy and complete the table of values for the relation y = 3x²−5x−7 for −3≤x≤4.
x: -3 -2 -1 0 1 2 3 4
y: ? ? ? -7 ? ? ? ?
(b) Using scales of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of y=3x²−5x−7 for −3≤x≤4.
(c) From your graph: (i) find the roots of the equation 3x²−5x−7=0; (ii) estimate the minimum value of y; (iii) calculate the gradient of the curve at the point x=2.

Accepted Answer

(a) Completed table (y=3x²−5x−7): x=−3: y=27+15−7=35; x=−2: y=12+10−7=15; x=−1: y=3+5−7=1; x=0: y=−7; x=1: y=3−5−7=−9; x=2: y=12−10−7=−5; x=3: y=27−15−7=5; x=4: y=48−20−7=21.

(b) The graph is a parabola (U-shaped curve) plotted from the table of values above, using the specified scales.

(c)(i) Roots of 3x²−5x−7=0 are found where the curve crosses the x-axis, at approximately x=−0.9 and x=2.6.
(ii) The minimum value of y, read from the lowest point of the curve, is approximately −9 (near x≈0.83).
(iii) Gradient at x=2: using values close to x=2 on the graph (e.g. Δy/Δx taken from x=1.5 to x=2.6), gradient r ≈ Δy/Δx = (1.5−(−10))/(1.5+10) ≈ 11.5/1.7 ≈ 6.8 (approximate value read from the graph).

WAEC Mathematics 2013 Theory — Question 7

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