Answer:
y = ax³ + bx² +cx +d (Main eq.)
Solve for a, b, c and d.
Solution:
y = 2x³ + x² -4x +6
Step-by-step explanation:
i) Solving for d:
Given point (0,6), at this point your x value is 0 and your y value is 6. Substitute the values on the Main Eq. above and you will find the d value to be 6.
ii) Solving for a, b & c.
Using points (-1,9),(1,5) and (2,18)
Substitute the given points on the Main Eq. above and you will have 3 equations with 3 unknown variables and solve the equations simultaneously to find your a, b & c.
Answer:
y = 2x³ + x² - 4x + 6
Step-by-step explanation:
General formula:
y = ax³ + bx² + cx + d
If you replace point (0, 6) in the general formula, you get:
6 = a(0)³ + b(0)² + c(0) + d
6 = d
If you replace points (-1, 9), (1, 5) and (2, 18) in the general formula, you get the following system of equations:
9 = a(-1)³ + b(-1)² + c(-1) + 6
9 = -a + b - c + 6 (eq. 1)
5 = a(1)³ + b(1)² + c(1) + 6
5 = a + b + c + 6 (eq. 2)
18 = a(2)³ + b(2)² + c(2) + d
18 = 8a + 4b + 2c + 6 (eq. 3)
Adding equation 1 to equation 2:
14 = 2b + 12
(14 - 12)/2 = b
b = 1
Multiplying equation 1 by 2:
18 = -2a + 2b - 2c + 12 (eq. 4)
Adding equation 4 to equation 3, and replacing with b value:
36 = 6a + 6b + 18
36 = 6a + 6 + 18
(36 - 6 - 18)/6 = a
a = 2
Replacing a and b values in equation 1:
9 = -2 + 1 - c + 6
c = -2 + 1 + 6 - 9
c = -4
