Theory question 107
Graphs of Functions(a)(i) Using a scale of 2 cm to 1 unit on both axes, on the same graph sheet, draw the graphs of y − 3x/4 = 3 and y + 2x = 6. (ii) From your graph, find the coordinates of the point of intersection of the two graphs. (iii) Show, on the graph sheet, the region satisfied by the inequality y − 3x/4 ≥ 3.
(b) Given that x2 + bx + 18 is factorized as (x + 2)(x + c). Find the values of c and b.
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(a)(i) y = 3x/4 + 3 passes through (0, 3) and (−4, 0); y = 6 − 2x passes through (0, 6) and (3, 0). Draw both lines.
(ii) 3x/4 + 3 = 6 − 2x → 11x/4 = 3 → x ≈ 1.1, y ≈ 3.8: about (1.1, 3.8).
(iii) The region on and above the line y = 3x/4 + 3 (shade it, or shade the unwanted side, as instructed).
(b) (x + 2)(x + c) = x2 + (2 + c)x + 2c. 2c = 18 → c = 9; b = 2 + 9 = 11.
Compare coefficients after expanding the brackets.