Theory question 108
Graphs of Functions(a) Copy and complete the table of values for the relation y = 5 − 7x − 6x2 for −3 ≤ x ≤ 2.
x: −3, −2, −1, −0.5, 0, 1, 2
y: −28, , 6, , 5, ,
(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the: (i) graph of y = 5 − 7x − 6x2 (ii) line y = 3 on the same axes.
(c) Use your graph to find the; (i) Roots of the equation 2 − 7x − 6x2 = 0 (ii) Maximum value of y = 5 − 7x − 6x2
Show the model answer
(a) x = −2: y = −5; x = −0.5: y = 7; x = 1: y = −8; x = 2: y = −33 (with −28, 6 and 5 given).
(b) Plot the points, join with a smooth upside-down parabola, and draw the horizontal line y = 3.
(c)(i) 2 − 7x − 6x2 = 0 is the same as 5 − 7x − 6x2 = 3, so read x where the curve meets y = 3: x ≈ −1.4 and x ≈ 0.2 (exact: −1.40 and 0.24).
(ii) Maximum value ≈ 7.0 (at x ≈ −0.6).
Rewrite the new equation so one side matches the drawn curve; the other side is the line to draw.