Theory question 107
Graphs of FunctionsThe table is for the relation y = px2 − 5x + q.
x: −3, −2, −1, 0, 1, 2, 3, 4, 5
y: 21, 6, __, −12, __, __, __, 0, 13
(a)(i) Use the table to find the values of p and q. (ii) Copy and complete the table.
(b) Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of the relation for −3 ≤ x ≤ 5.
(c) Use the graph to find: (i) y when x = 1.8; (ii) x when y = −8.
Show the model answer
(a)(i) At x = 0, y = −12, so q = −12. At x = 4: 16p − 20 − 12 = 0 → p = 2. So y = 2x² − 5x − 12.
(ii) x = −1: y = −5; x = 1: y = −15; x = 2: y = −14; x = 3: y = −9
(b) Plot the nine points with the given scales and join them with a smooth U-shaped curve (minimum near x = 1.25, y ≈ −15.1).
(c)(i) y ≈ −14.5 (exact −14.52)
(ii) x ≈ −0.6 or x ≈ 3.1 (roots of 2x² − 5x − 4 = 0)
Find q first from the point where x = 0.