Theory question 107
Graphs of Functions(a) Copy and complete the table of values for the relation y = 2x2 − x − 2 for −4 ≤ x ≤ 4.
x: −4, −3, −2, −1, 0, 1, 2, 3, 4
y: __, 19, __, __, −2, __, __, __, 26
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 2x2 − x − 2 for −4 ≤ x ≤ 4.
(c) On the same axis, draw the graph of y = 2x + 3.
(d) Use the graph to find the: (i) roots of the equation 2x2 − 3x − 5 = 0; (ii) range of values of x for which 2x2 − x − 2 < 0.
Show the model answer
(a) y = 34, 19, 8, 1, −2, −1, 4, 13, 26
(b) Plot the points and draw a smooth U-shaped curve
(c) Straight line through e.g. (−4, −5), (0, 3), (4, 11)
(d)(i) 2x2 − 3x − 5 = 0 is where the curve meets y = 2x + 3: x = −1 and x = 2.5
(ii) The curve is below the x-axis between its x-intercepts: about −0.8 < x < 1.3
Subtracting 2x + 3 from the curve's equation gives 2x2 − 3x − 5, so the intersections give its roots.