WRITING CUBIC FUNCTIONS FROM GIVEN INFORMATION WORKSHEET

Find the equation of the cubic whose graph :

Problem 1 :

Cuts the x - axis at 3, 1, -2 and passes through (2, -4)

Solution

Problem 2 :

Cuts the x - axis at -2, 0 and 1/2 and passes through (-3, -21)

Solution

Problem 3 :

Touches the x - axis at 1, cuts the x- axis at -2 and passes through (4, 54)

Solution

Problem 4 :

Touches the x - axis at -2/3, cuts the x- axis at 4 and passes through (-1, -5)

Solution

Find the equation of a real cubic polynomial which cuts :

Problem 5 :

The x - axis at 1/2 and -3, cuts the y - axis at 30 and passes through (1, -20)

Solution

Problem 6 :

The x  - axis at 1, touches the x - axis at -2 and cuts the y - axis at (0, 8)

Solution

Problem 7 :

The x - axis at 2, the y- axis at -4 and passes through (1, -1) and (-1, -21)

Solution

Answer Key

1)  P(x) = (x - 3) (x - 1) (x + 2) 

2)  P(x) = 2(x + 2) (x) (x - 1/2)

3)  P(x) = (x - 1)2 (x + 2)

4)   (3x + 2)2 (x - 4)

5)  P (x) = 5(2x - 1) (x + 3) (x - 2)

6)  P(x) = -2 (x - 1) (x + 2)2

7)  P(x) = (x - 2) (2x2 - 3x + 2)

Find the equation of the cubic with graph :

Problem 1 :

equofthecubic

Solution

Problem 2 :

equofthecubic2

Solution

Problem 3 :

equofthecubic3

Solution

Problem 4 :

equofthecubic4

Solution

Problem 5 :

equofthecubic5

Solution

Problem 6 :

equofthecubic6

Solution

Answer Key

1)  P(x) = 2 (x + 1) (x - 2) (x - 3)

2)  P(x) = -2 (x + 3) (2x + 1) (2x - 1)

3)  P(x) = 1/4 (x + 4)2 (x - 3)

4)  P(x) = 1/10 (x + 5) (x + 2) (x - 5)

5)  P(x) = 1/4 (x + 4) (x - 3)2

6) P(x) = -2 (x + 3) (x + 2 ) (2x + 1) 

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