Theory question 113
Graphs of Functions(a) Copy and complete the table. y = x2 − 2x − 2 for −4 ≤ x ≤ 4.
x: −4, −3, −2, −1, 0, 1, 2, 3, 4
y: 22, , , , −2, , , 1, 6
(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 = x2 − 2x − 2.
(c) Use your graph to find: (i) the roots of the equation x2 − 2x − 2 = 0; (ii) the values of x for which x2 − 2x − 4½ = 0 (iii) the equation of the line of symmetry of the curve.
Show the model answer
Model answer
(a) x = −3: 13; −2: 6; −1: 1; 1: −3; 2: −2.
(b) Plot and join with a smooth U-shaped curve (lowest point (1, −3)).
(c)(i) The curve crosses y = 0 at x ≈ −0.7 and x ≈ 2.7.
(ii) x2 − 2x − 4½ = 0 means x2 − 2x − 2 = 2½; draw y = 2.5: x ≈ −1.3 and x ≈ 3.3.
(iii) x = 1.
Explanation
The line of symmetry passes through the lowest point of the curve.