Question

10. (a) Copy and complete the table of values for y=2x^2-4x-3, -2<=x<=6. (b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of y=2x^2-4x-3. (c) Use your graph to find: i. Roots of 2x^2-4x-3=4 correct to 1 decimal place ii. Gradient of the curve at x=4. (12 marks)

Accepted Answer

(a) Substituting each x-value from -2 to 6 into y=2x^2-4x-3 gives the completed table (e.g. x=-2: y=13; x=0: y=-3; x=2: y=-3; x=4: y=13; x=6: y=45).
(b) Plot the computed points on graph paper using the given scale and draw a smooth curve through them.
(c)(i) The roots of 2x^2-4x-3=4 (i.e. 2x^2-4x-7=0) are read from where the curve crosses the line y=4; algebraically x = (4 +/- sqrt(16+56))/4 = (4 +/- sqrt72)/4, giving approximately x=-1.1 and x=3.1 (to 1 d.p.).
ii. The gradient of the curve at x=4 is estimated by drawing a tangent to the curve at that point; algebraically dy/dx=4x-4, so at x=4 the gradient is 12, which should closely match the graphical estimate.

NECO Mathematics 2025 Theory — Question 10

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