Theory question 111
Graphs of Functions(a) Copy and complete the table of values for y = 2x2 + x − 10 for −5 ≤ x ≤ 4.
x: −5, −4, −3, −2, −1, 0, 1, 2, 3, 4
y: __, __, 5, __, −9, −10, __, 0, __, __
(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 y = 2x2 + x − 10 for −5 ≤ x ≤ 4.
(c) Use the graph to find the solution of: (i) 2x2 + x = 10; (ii) 2x2 + x − 10 = 2x.
Show the model answer
Model answer
(a) x = −5: 35; −4: 18; −2: −4; 1: −7; 3: 11; 4: 26
(b) Plot the points and join with a smooth U-shaped curve.
(c)(i) 2x² + x − 10 = 0: where the curve cuts the x-axis, x = −2.5 or x = 2
(ii) Draw the line y = 2x; it meets the curve at x = −2 and x = 2.5
Explanation
For (c)(ii) draw the straight line y = 2x on the same axes.