Porisma

A hint to get started

Use completing the square before drawing a rational graph

C:y=f(x)C:y=f(x) where f(x)=(4x2+bx+c)/(4x+8)f(x)=(4x^2+bx+c)/(4x+8) and b,c are real constants. C has oblique asymptote y=x−5.

(i) Find b. marks

(ii) Given c>9, show C does not cut the x-axis. mark

(iii) For c=13 sketch C, clearly indicating asymptotes, axial intercepts and turning points. marks

[2012/SRJC/Promo/8]

CJC · Review problems · Question 8

A strictly positive completed square rules out numerator zeros.

Read the worked solution