# Download A Hat to Fit Bun by Joanne Wachter illustrated by Laura Logan PDF

By Joanne Wachter illustrated by Laura Logan

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12 ax2 + (3 ¡ a)x ¡ 4 = 0 has roots which are real and positive. What values can a have? 13 a Determine the equation of: i the quadratic function ii the straight line. y -3 b For what values of x is the straight line above the curve? 3 x -27 14 Show that the lines with equations y = ¡5x + k y = x2 ¡ 3x + c if and only if c ¡ k = 1. are tangents to the parabola cyan magenta yellow 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 15 4x2 ¡ 3x ¡ 3 = 0 has roots p, q. Find all quadratic equations with roots p3 and q3 .

Ym a Explain why 9x + 8y = 1800: b Show that the area of each pen is given by A = ¡ 98 x2 + 225x m2 . xm c If the area enclosed is to be maximised, what are the dimensions of each pen? y = x2 - 3x x 3 cyan magenta yellow 95 100 50 75 25 95 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 y = 2x - x2 0 b Find the maximum vertical separation between the curves for 0 6 x 6 2 12 . 5 2 The graphs of y = x2 ¡ 3x and y = 2x ¡ x2 are illustrated. a Without using technology, show that the graphs meet where x = 0 and x = 2 12 .

Find: a f ±g b g ± f. 7 Given f(x) = x+3 x+2 and g(x) = a (f ± g)(x) x+1 , x¡1 find in simplest form: b (g ± f )(x) c (g ± g)(x) cyan magenta yellow 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 In each case, find the domain of the composite function. cdr Monday, 20 February 2012 1:41:56 PM BEN IB_HL-3ed 64 FUNCTIONS (Chapter 2) 8 Given f(x) = p 1 ¡ x and g(x) = x2 , find: a (f ± g)(x) 9 b the domain and range of (f ± g)(x) a If ax + b = cx + d for all values of x, show that a = c and b = d.

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