Posted by jun on Monday, January 24, 2011 at 12:34pm.
With regards to question J:
The variables x and y are connected by the equation y = x2 - x - 5. Some corresponding values of x and y are given in the table below.
x -4 -3 -2 -1 0 1 2 3 4 5
y 15 7 a -3 -5 b -3 1 7 15
(a) Calculate the values of a and b
(b) Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent
1 unit on the y-axis, draw the graph of y = x2 - x - 5 for
- 4 £ x £ 5.
(c) Use the graph to find
(i) the value of y when x = - 3.5
(ii) the values of x when y = - 2
(iii) the minimum value of y
(iv) the values of x when y = 0
(v) the value of y when x = 0
(vi) the range of values of y when -2 < x < 2
(d) By drawing a suitable straight line to intersect the curve graph,
find the solutions to the equation
(i) x2 - x - 5 = 0
(ii) x2 - x - 5 = 2x + 1
(iii) x2 - x = 8
(e) Use your graph to solve the inequality x2 - x - 5 > 2x + 1
(f) By drawing a tangent, find the gradient of the curve y = x2 - x - 5
at the point (2, -3)
(g) By drawing a suitable tangent to the curve, find the co-ordinates of
the point A at which the gradient of the tangent at A is 1
(h) From the graph, find the values of x for which the gradient is positive.
(i) Describe fully the symmetry of the graph.
(j) Find the cubic equation which is satisfied by the x values of the intersecting point of the curve x2 - x - 5 and the curve 1/x
How do one go about solving it?
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