10. Procedures: Step (2): we have y = ( x – 2)( x – 3) , i.e. y = 0, when x = 2 or x = 3. Factorize x 2 – 5 x + 6, The corresponding quadratic function is y = x 2 – 5 x + 6 Sketch the graph of y = x 2 – 5 x + 6. Step (1): Step (3): Step (4): Find the solution from the graph.
11. Sketch the graph y = x 2 – 5 x + 6 . What is the solution of x 2 – 5 x + 6 > 0 ? x y 0 y = ( x – 2)( x – 3) , y = 0, when x = 2 or x = 3. 2 3
12. x y 0 We need to solve x 2 – 5 x + 6 > 0, The portion of the graph above the x-axis represents y > 0 (i.e. x 2 – 5 x + 6 > 0) The portion of the graph below the x-axis represents y < 0 (i.e. x 2 – 5 x + 6 < 0) above the x-axis. so we choose the portion 2 3
13. x y 0 When x < 2 , the curve is above the x-axis i.e., y > 0 x 2 – 5x + 6 > 0 When x > 3 , the curve is above the x-axis i.e., y > 0 x 2 – 5x + 6 > 0 2 3