Theory question 114
Graphs of Functions(Questions 14 and 15 are for candidates in Ghana, Sierra Leone and The Gambia only.)
(a) The function f is defined as f: x → 3x2 − 5x. (i) Evaluate f(−2). (ii) Find the values of x for which f(x) = −7/4.
(b) A rhombus ABCD has A at (0, 2) and B at (5, 3). If the diagonals intersect at (0, 3), find the coordinates of C and D.
Show the model answer
Model answer
(a)(i) f(−2) = 3(4) + 10 = 22.
(ii) 3x2 − 5x = −7/4 → 12x2 − 20x + 7 = 0 → (6x − 7)(2x − 1) = 0 → x = 7/6 or x = ½.
(b) The diagonals bisect each other at M(0, 3). C = 2M − A = (0, 4); D = 2M − B = (−5, 3).
Explanation
The point where the diagonals meet is the midpoint of AC and of BD.