Theory question 108
Graphs of Functions(a) Copy and complete the following table of values for the relation y = x2 − 2x − 5.
x: −3, −2, −1, 0, 1, 2, 3, 4, 5
y: , , −2, , −6, , −2, 3, 10
(b) Draw the graph of the relation y = x2 − 2x − 5, using a scale of 2cm to 1 unit on the x-axis, and 2cm to 2 units on the y-axis.
(c) Using the same axes, draw the graph of y = 2x − 3.
(d) Obtain in the form ax2 + bx + c = 0 where a, b and c are integers, the equation which is satisfied by the x-coordinate of the points of intersection of the two graphs.
(e) From your graphs, determine the roots of the equation obtained in (d) above.
Show the model answer
(a) x = −3: 10; x = −2: 3; x = 0: −5; x = 2: −5.
(b) Plot and join with a smooth U-shaped curve (lowest point (1, −6)).
(c) Straight line through (0, −3) and (3, 3).
(d) x2 − 2x − 5 = 2x − 3 gives x2 − 4x − 2 = 0.
(e) Read the x-values where the line meets the curve: x ≈ −0.4 and x ≈ 4.4 (exact 2 ± √6 = −0.45, 4.45).
At an intersection both equations give the same y, so set them equal.