# The Physics Behind the Psychology of the Human Mind and Frog Ribcage Breastfeeding a Piglet

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Name: ______________________________ ( ) Date: ___________ Class: __________ Revision (Quadratic Equations and Functions) Question 1 Find the values of k for which the equation x2 + 2x + 16 = 3kx has equal roots. Question 2 Find the range of values of p such that x 2 + ( p − 3) x + p + 5 > 0 for all values of x. Question 3 Show that the equation (p + 1)x2 + (2p + 3)x + (p + 2) = 0 has real roots for all real values of p. Question 4 Find the smallest integer value of m for which the expression 2 x 2 − 5 x + m will always be positive for all real values of x. Question 5 Find the range of values of m for which the equation 6 x 2 − 3x − 5m = 0 has no real roots. Question 6 Find the range of values of m for which 2x2 + 5x + m is always positive for all real values of x. Question 7 x2 Find the values of k for which the equation = 1 − x has 2 real distinct roots. k −2 Question 8 Find the values of p for which the equation ( p − 2) x 2 − px + 1 + 2 x = 0 has equal roots. Question 9 (a) Express x 2 + 6 x − 7 in the form ( x − h) 2 + k . (b) Hence solve the equation x 2 + 6 x − 7 = 0 . (c) (i) Sketch the graph y = x 2 + 6 x − 7 . (ii) Mark and label the coordinates of the points where the graph cuts the axes. (iii) Write down the equation of the line of symmetry. Question 10 Given that the curve y = x 2 + ax − b crosses the x-axis at values of a and b. . Find the 1 Question 11 (a) Given that ( x − 3)( x + 4) = ( x + a) 2 − b , state the values of a and b. (b) Sketch the graph of y = ( x − 3)( x + 4) on the given axes below. You must show clearly the x and y intercept and the line of symmetry. y x Question 12 The diagram shows the graph of the curve y = ( x + k )(2 − x) , where k is a constant. The curve meets the y axis at A and the x axis at B and C as shown. (a) Write down the coordinates of B and find the value of k. (b) Find the coordinates of A. (c) Write down