Theory question 102
Graphs of Functions(a) The graph of y = 2px2 − p2x − 14 passes through the point (3, 10). Find the values of p.
(b) Two lines, 3y − 2x = 21 and 4y + 5x = 5, intersect at the point Q. Find the coordinates of Q.
Show the model answer
Model answer
(a) 10 = 18p − 3p² − 14 → 3p² − 18p + 24 = 0 → p² − 6p + 8 = 0 → (p − 2)(p − 4) = 0
p = 2 or p = 4
(b) ×4 and ×3: 12y − 8x = 84 and 12y + 15x = 15 → 23x = −69 → x = −3
4y − 15 = 5 → y = 5; Q = (−3, 5)
Explanation
Substitute x = 3 and y = 10 to get a quadratic in p.