) Show that the solutions of the equation (x^2 – 6x – 43 = 0) can be written in the form (x = p pm frac{qsqrt{13}}{13}), where (p) and (q) are positive integers.
(4 points)
b) Based on the above or any other method, solve the inequality (x^2 – 6x – 43 le 0).
(2 points)
**16. P1:**
A function (f) is defined by (f(x) = 3(x-1)^2 – 18), (x in mathbb{R}).
a) Write (f(x)) in the form (ax^2 + bx + c), where (a), (b), and (c) are constants.
(2 points)
b) Find the coordinates of the vertex of the graph of (f).
(1 point)
c) Find the equation of the axis of symmetry of the graph of (f).
(1 point)
d) Indicate the range of (f).