Introduction: This is a major question in Paper II, often worth 10 marks. Accuracy is key. Use a sharp pencil and be careful when plotting points. Most marks are for interpreting the graph correctly, so practice answering all the standard question types.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Plotting): Given the function y=x2−4x and the value x=3, calculate the corresponding y-value.

• Prompt 2 (Identify): From a drawn graph of a parabola, identify the coordinates of the turning point (vertex).

• Prompt 3 (Identify): Is the turning point a maximum or a minimum for the function y=−2x2+...? Why?

• Prompt 4 (Method): How do you find the roots of the equation x2−4x=0 from the graph of the function y=x2−4x?

• Prompt 5 (Method): How do you solve the simultaneous equations y=2x+1 and y=−x+4 graphically?

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Task): Draw the graph of the function y=x2−6x+5 for the range of values 0≤x≤6.

• Prompt 2 (Analysis): Using the graph from the previous prompt, find:

  • The minimum value of the function.

  • The equation of the axis of symmetry.

  • The roots of the equation x2−6x+5=0.

• Prompt 3 (Analysis): Find the range of values of x for which the function y=x2−6x+5 is negative.

• Prompt 4 (Analysis): Find the range of values of x for which the function y=x2−6x+5 is decreasing.

• Prompt 5 (Sketch): Without drawing an accurate graph, sketch the graph of y=−(x−2)2+3, marking the coordinates of the turning point and the y-intercept.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Task): Draw the graph of y=3+2x−x2 for −2≤x≤4.

• Prompt 2 (Analysis): Using the graph, find the range of values of x for which y is positive and increasing.

• Prompt 3 (Analysis): For the function y=3+2x−x2, find the values of x when y = 1.

• Prompt 4 (Deduction): Using the graph of y=x2−6x+5, find the roots of the equation x2−6x+8=0. (Hint: Draw the line y=3).

• Prompt 5 (Word Problem): The height (h metres) of a ball thrown upwards after t seconds is given by h=20t−5t2. Draw a graph for 0≤t≤4 and find the maximum height reached by the ball.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Deduction): Use your graph of y=x2−6x+5 to find the roots of 2x2−12x+10=0. Explain your method.

• Prompt 2 (Synthesis): Given the function y=(x−a)2+b, the coordinates of its turning point are (3, -4). Write down the function. Then, find the roots of the equation (x−a)2+b=0.

• Prompt 3 (Analysis): The graph of a quadratic function intersects the x-axis at (-2, 0) and (4, 0) and passes through the point (1, -9). Find the equation of the function.

• Prompt 4 (Challenge): Describe the transformation that maps the graph of y=x2 onto the graph of y=x2+4x+1.

• Prompt 5 (Word Problem): A rectangular plot has a perimeter of 40m. If its length is x, show that its area A is given by A=x(20−x). Draw the graph of this function and find the length that gives the maximum possible area.