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Maths B Assignment

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Mathematics B Assignments: Functions
Task 1. (KPS, MPS) i) With K=0, determine the function and sketch it on a suitable domain.
Point A: (1, 4)
Point B: (2, 2)
Point C: (4, k) or (4, 0)

Using the equation y = ax² + bx + c substitute the 3 points (x and y) into three equations to find the function.

Point A: 1…………… 4 = 1x + 1x + 1c
Point B: 2…………….2 = 4x + 2x + 1c
Point C: 3…………….0 = 16x + 4x + 1c

Using the simultaneous equation function on the graphics calculator, find the function of the three points and graph using Autograph. Function = y = 0.3333x² - 3x + 6⅔ ii) Systematically vary k and explore the effect of k on the behaviour of the quadratic functions produced.

Point A: (1, 4)
Point B: (2, 2)
Point C: (4, x)

Use the quadratic function y = ax² + bx + c and substitute the points into the equation to find the functions. Vary the x value to explore the effect of k in the graph.

Point A: 1…………… 4 = 1x + 1x + 1c Point B: 2…………… 2 = 4x + 2x + 1c Vary points C using -3 to 3 Y value | Point C: Equation 3 | Functions | Y = 3 | 3 = 16x + 4x + 1c | y = 0.8333x² - 4.5x + 7.666 | Y= 2 | 2 = 16x + 4x + 1c | y = 0.6666x² - 4x + 7.333 | Y= 1 | 1 = 16x + 4x + 1c | y = 0.5x² - 3.5x + 7 | Y = 0 | 0 = 16x + 4x + 1c | Y = 0.3333x² - 3x + 6.666 | Y= -1 | -1 = 16x + 4x + 1c | y = 0.6666x² - 2.5x + 6.333 | Y =-2 | -2 = 16x + 4x + 1c | y = 0x²-2x + 6 | Y = -3 | -3 = 16x + 4x + 1c | y = 0.166x² - 1.5x + 5.666 |

From the above graph we can see that by varying the value of ‘k’ will

Task 2. (KPS, MPS) i) Explore the effects of d on the behaviour of the cubic functions.

Point A: (1, 4)
Point B: (2, 2)
Point C: (4, 1.5) Point D is randomly selected: (5, 4)

Using the four points substitute values into the cubic function y = ax³ + bx² + cx + d in order to produce 4

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