Copy and complete the table of values for the equation y = x 3 - 6 x 2 + 8 x x - 1 - 0 . 5 0 0 . 5 1 . 5 1 2 . 5 3 3 . 5 4 4 . 5 5 y = x 3 - 6 x 2 + 8 x

Given graph: y = x 3 - 6 x 2 + 8 x We can find the values of y for different values of x . Example, for x = - 1 , y = x 3 - 6 x 2 + 8 x = - 1 3 - 6 - 1 2 + 8 - 1 = - 15 . for x = - 0 . 5 , y = - 0 . 5 3 - 6 - 0 . 5 2 + 8 - 0 . 5 = - 5 . 6 for x = 0 , y = 0 for x = 0 . 5 , y = 0 . 5 3 - 6 × 0 . 5 2 + 8 0 . 5 = 2 . 6 for x = 1 , y = 1 3 - 6 1 2 + 8 × 1 = 3 for x = 1 . 5 , y = 1 . 5 3 - 6 1 . 5 2 + 8 × 1 . 5 = 1 . 9 for x = 2 , y = 2 3 - 6 2 2 + 8 × 2 = 0 for x = 2 . 5 , y = 2 . 5 3 - 6 2 . 5 2 + 8 × 2 . 5 = - 1 . 9 for x = 3 , y = 3 3 - 6 3 2 + 8 × 3 = - 3 for x = 3 . 5 , y = 3 . 5 3 - 6 3 . 5 2 + 8 × 3 . 5 = - 2 . 6 for x = 4 , y = 4 3 - 6 4 2 + 8 × 4 = 0 for x = 4 . 5 , y = 4 . 5 3 - 6 4 . 5 + 8 × 4 . 5 = 5 . 6 for x = 5 , y = 5 3 - 6 × 5 2 + 8 × 5 = 15 Thus, we can complete the table. x - 1 - 0 . 5 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5 4 4 . 5 5 y = x 3 - 6 x 2 + 8 x - 15 - 5 . 6 0 2 . 6 3 1 . 9 0 - 1 . 9 - 3 - 2 . 6 0 5 . 6 15

Draw the graph of y = x 3 10 and y = 6 x - x 2 for - 4 ⩽ x ⩽ 6

Given equations: y = x 3 10 and y = 6 x - x 2 The table of points for the graph with - 4 ⩽ x ⩽ 6 is shown below: x - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 y = x 3 10 - 6 . 4 - 2 . 7 - 0 . 8 - 0 . 1 0 0 . 1 0 . 8 2 . 7 6 . 4 12 . 5 21 . 6 y = 6 x - x 2 - 40 - 27 - 16 - 7 0 5 8 9 8 5 0 The graphs are shown here:

Use the graphs to solve the equation x 3 10 + x 2 - 6 x = 0

Given equation: x 3 10 + x 2 - 6 x = 0 We can consider, two graphs y = x 3 10 and y = 6 x - x 2 We have to find the x - values of the points of intersection of the two curves. The co-ordinates of the two points of intersection are 0 , 0 and 4 . 2 , 7 . 56 . So, the x - values of the points of intersection are x = 0 and x = 4 . 2 .

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Algebra>Chapter 18 - Curved Graphs>Exercise 18.7

Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 18.7

Author:Karen Morrison & Nick Hamshaw

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 18.7

Attempt the practice questions from Exercise 7: Exercise 18.7 with hints and solutions to strengthen your understanding. Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition solutions are prepared by Experienced Embibe Experts.