Question 10:
(a) Complete the table in the answer space for the equation y = x3 – 13x + 18 by writing down the values of y when x = –2 and x = 3.
(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By 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 = x3 – 13x + 18 for –4 ≤ x ≤ 4 and 0 ≤ y ≤ 40.
(c) From your graph, find
(i) the value of y when x = –1.5,
(ii) the value of x when y = 25.
(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x3 – 11x – 2 = 0 for –4 ≤ x ≤ 4 and 0 ≤ y ≤ 40.
Answer:
Solution:
(a)
y = x3 – 13x + 18
when x = –2,
y = (–2)3 – 13(–2) + 18
= –8 + 26 + 18
= 36
when x = 3,
y = (3)3 – 13(3) + 18
= 27 – 39 + 18
= 6
(b)
(c)
(i) From the graph, when x = –1.5, y = 34.
(ii) From the graph, when y = 25, x = –3.25, –0.55 and 3.85.
(d)
y = x3 – 13x + 18 ----- (1)
0 = x3 – 11x – 2 ----- (2)
(1) – (2) : y = –2x + 20
The suitable straight line is y = –2x + 20.
Determine the x-coordinates of the two points of intersection of the curve y = x3 – 13x + 18 and the straight line y = –2x + 20.
From the graph, x = –3.2, –0.2 and 3.4.
(a) Complete the table in the answer space for the equation y = x3 – 13x + 18 by writing down the values of y when x = –2 and x = 3.
(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By 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 = x3 – 13x + 18 for –4 ≤ x ≤ 4 and 0 ≤ y ≤ 40.
(c) From your graph, find
(i) the value of y when x = –1.5,
(ii) the value of x when y = 25.
(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x3 – 11x – 2 = 0 for –4 ≤ x ≤ 4 and 0 ≤ y ≤ 40.
Answer:
Solution:
(a)
y = x3 – 13x + 18
when x = –2,
y = (–2)3 – 13(–2) + 18
= –8 + 26 + 18
= 36
when x = 3,
y = (3)3 – 13(3) + 18
= 27 – 39 + 18
= 6
(b)
(c)
(i) From the graph, when x = –1.5, y = 34.
(ii) From the graph, when y = 25, x = –3.25, –0.55 and 3.85.
(d)
y = x3 – 13x + 18 ----- (1)
0 = x3 – 11x – 2 ----- (2)
(1) – (2) : y = –2x + 20
The suitable straight line is y = –2x + 20.
Determine the x-coordinates of the two points of intersection of the curve y = x3 – 13x + 18 and the straight line y = –2x + 20.
From the graph, x = –3.2, –0.2 and 3.4.