Theory question 108
Graphs of Functions(a) Copy and complete the table of values for y = 2x2 − x − 4 for −3 ≤ x ≤ 3.
x: −3, −2, −1, 0, 1, 2, 3
y: 17, __, __, −4, __, __, __
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of y = 2x2 − x − 4 for −3 ≤ x ≤ 3.
(c) Use the graph to find the: (i) roots of the equation 2x2 − x − 4 = 0; (ii) values of x for which y increases as x increases. (iii) minimum point of y.
Show the model answer
Model answer
(a) y = 17, 6, −1, −4, −3, 2, 11
(b) Plot the points and join with a smooth U-shaped curve
(c)(i) Where the curve crosses the x-axis: x ≈ −1.2 and x ≈ 1.7
(ii) y increases for x > 0.25 (about x > 0.2 from the graph)
(iii) Minimum point ≈ (0.25, −4.1)
Explanation
The roots are where the curve cuts the x-axis; the lowest point is the minimum.