Alevel_C1C2

3
Exam-style assessment
Quadratic functions
1. (a) Given that x 2 + 6x + 4 º (x + a) 2 + b, where a and b are constants, find the
value of a and the value of b. (2)
(b) Show that the roots of x 2 + 6x + 4 = 0 can be written in the form p ± q 5
and determine the value of p and the value of q. (4)
2. (a) Solve the quadratic equation 4x 2 - 2x - 1 = 0, writing your answers in a
simplified surd form. (2)
(b) Show, by completing the square, that the quadratic can be written in the form
4x 2 - 2x - 1 = 4[(x + a) 2 + b]
and hence determine the values of a and b. (4)
3. Sketch the curve given by the equation y = x(x – 4) for -1 x 5
(a) Write down the coordinates of the points where the curve intersects the x-axis (4)
(b) Find the coordinates of the turning point indicating the nature of the
turning point. (2)
4. Sketch the graph of y = x 2 and the graph of y = 8 - 2x on the same axes taking
values of x from -5 to +3.
Show how you use your graph to solve the equation x 2 + 2x - 8 = 0 and hence
determine the solutions. (7)
5. (a) The equation 4x 2 + ax + 9 = 0 has equal roots; find the value of a given
that a < 0. (3)
(b) The equation 9x 2 + 3kx + k = 0 has equal roots where k ¹ 0; find the value of k. (4)
© Oxford University Press 2008
Core C1