Theory question 107
Graphs of Functions(a) Copy and complete the table of values for the equation y = 2x2 − 7x − 9 for −3 ≤ x ≤ 6.
x: −3, −2, −1, 0, 1, 2, 3, 4, 5, 6
y: __, 13, __, −9, −14, __, −12, __, 6, __
(b) using scales of 2cm to 1 unit on the x-axis and 2cm to 4 units on the y-axis, draw the graph of y = 2x2 − 7x − 9 for −3 ≤ x ≤ 6.
(c) Use the graph to estimate the: (i) roots of equation 2x2 − 7x = 26; (ii) coordinates of the minimum point of y; (iii) range of values for which 2x2 − 7x < 9.
Show the model answer
(a) x = −3: 30; x = −1: 0; x = 2: −15; x = 4: −5; x = 6: 21
(b) Plot the points and join with a smooth U-shaped curve.
(c)(i) 2x² − 7x − 9 = 17: draw y = 17; x ≈ −2.3 and x ≈ 5.8
(ii) Minimum point ≈ (1.75, −15.1)
(iii) 2x² − 7x − 9 < 0 where the curve is below the x-axis: −1 < x < 4.5
For (c)(i), rewrite the equation so the left side matches y and draw the horizontal line y = 17.