Theory question 110
Graphs of FunctionsThe following is an incomplete table for the relation y = 2x2 − 5x + 1
x: −3, −2, −1, 0, 1, 2, 3, 4, 5
y: _, _, 8, 1, −2, _, _, _, 26
(a) Copy and complete the table.
(b) Using a scale of 2cm to 1 unit on the x axis and 2cm to 10 units on the y axis, draw a graph of the relation y = 2x2 − 5x + 1 for −3 ≤ x ≤ 5.
(c) Using the same scale and axes, draw the graph of y = x + 6.
(d) Estimate from your graphs, correct to one decimal place: (i) the least value of y and the value of x for which it occurs; (ii) the solution of the equation 2x2 − 5x + 1 = x + 6.
Show the model answer
(a) y = 34, 19, 8, 1, −2, −1, 4, 13, 26
(b) Smooth U-shaped curve through the plotted points with the given scales
(c) Straight line through e.g. (−3, 3), (0, 6), (5, 11)
(d)(i) Least value of y ≈ −2.1 at x ≈ 1.3 (exact: −2.125 at x = 1.25)
(ii) Read x at the intersections: x ≈ −0.7 or x ≈ 3.7 (since 2x2 − 6x − 5 = 0)
The solutions of the equation are the x-values where the curve and the line cross.