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Alternative method: Equation of graph: y = x 2 – 3x + 2 Equation to be solved: 0 = x 2 – 3x + 1 Subtracting: y = 1 is the equation of the line to be drawn. (c) Use the above graph to solve x 2 – 4x = 0 y = x 2 – 3x + 2 0 = x 2 – 4x (subtracting) y = x + 2 Draw a straight line graph of the function y = x + 2 on the same axes as shown below: The line crosses the curve at the points where x = 0 and x = 4. Hence the solutions of x 2 – 4x = 0 are x = 0 and x = 4.
Range of values (Use graph of example 2.18) Example Find the range of values of x for which the function x 2 – 3x + 2 (a) is negative, (b) is less than (x + 2), (c) is greater than 1. Solution (a) x 2 – 3x + 2 is negative (i.e. below the x-axis) for values of x from 1 to 2. The range is 1 < x < 2. (b) x 2 – 3x + 2 is less than x + 2 (i.e. below the line y = x + 2) fro x = 0 to x = 4, i.e. 0 < x < 4. (c) In the given domain -1 ≤ x ≤ 4, the function x 2 – 3x + 2 is greater than 1 in two ranges: From -1 to 0.4 and from 2.6 to 4, i.e. -1 < x < 0.4 and 2.6 < x < 4. Intersecting graphs Example Draw the graph of y = 1 + x – 2x 2 , taking values of x in the domain -3 ≤ x ≤ 3. Using the same scale and axes, draw the graph of y = 2x – 5. Use your graphs to answer the following questions: (a) What is the maximum value of the function 1 + x – 2x 2 ? (b) Write down the x-coordinates of the points of intersection of the functions y = 1 + x – 2x 2 and y = 2x – 5. Show that these values of x satisfy the equation 2x 2 + x – 6 = 0. Table of values for y = 1 + x – 2x 2 x -3 -2 -1 0 1 2 3 1 1 1 1 1 1 1 1 x -3 -2 -1 0 1 2 3 -2x 2 -18 -8 -2 0 -2 -8 -18 y -20 -9 -2 1 0 -5 -14 Table for y = 2x – 5 x -3 0 3 y -11 -5 1 When plotted, a curve and a straight line as shown in the figure below are obtained.
Page 1 and 2: QUADRATIC EXPRESSIONS AND EQUATIONS
Page 3 and 4: 1. (x + 3)(x + 1) 2. (x + 2)(x - 4)
Page 5 and 6: Area of square A = b 2 Area of rect
Page 7 and 8: Similarly: (a) (x + 3)(x + 4) = x(x
Page 9 and 10: Exercise Factorize: 1. x 2 + 7x + 1
Page 11 and 12: (e) 94 × 106 (f) 975 × 1,025 (g)
Page 13 and 14: Factorizing x 2 - 16x + 64 = 0 give
Page 15 and 16: Example Factorize x 2 + 7x + 6 = 0.
Page 17 and 18: x = 3 1 or x = 7 Exercise : Solve.
Page 19 and 20: 21. 2y 2 1 - 5y + 1 = 0 22. y 2 +3y
Page 21 and 22: 6. The perimeter of a rectangle is
Page 23 and 24: Example Draw the graphs of y = x 2
Page 25: Graphical solution of equations (Us
Page 29 and 30: What transformation will map the fi
Page 31: (a) Draw suitable straight lines to

J17

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