Page 33 - Math SL HB Sem 2

3. The equation ofa curve may be written in the form y = a(x p)(x - q). The curve intersects the
-
;-axis at A(-2, 0) and B(4, 0). The curve ofy =/(.r) is shown in the diagram below.

4

2

B
4 6 -I

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(a) (D Write down the value ofp and of q.

(iD Given that the point (6, 8) is on the curve, find the value ofa.

(iiD Write the equation of the curve in the form y: a? + bx + c.
(s)

(b) (i) rina s

(ii) A tangent is drawn to the curve at a point P. The gradient ofthis tangent is 7.
Find the coordinates of P.
(4)

(") The line Z passes through B(4, 0), and is perpendicular to the tangent to the curve at
point B.
(D Find the equation ofI.

(ii) Find the x-coordinate ofthe point where Z intersects the curve again.
(6)
(Total l5 marks)

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