Find a polynomial function whose graph passes through (1,-2) (0,1) (1,2) (2,17)
the polyynomial function is y=
To find the polynomial function that passes through these given points, we can use the method of interpolation.
Let's start by writing the general form of a polynomial function:
y = ax^3 + bx^2 + cx + d
Substitute the x and y values from the given points into the function to create a system of equations:
Equation 1: -2 = a(1)^3 + b(1)^2 + c(1) + d
Equation 2: 1 = a(0)^3 + b(0)^2 + c(0) + d
Equation 3: 2 = a(1)^3 + b(1)^2 + c(1) + d
Equation 4: 17 = a(2)^3 + b(2)^2 + c(2) + d
Simplify these equations:
Equation 1: -2 = a + b + c + d
Equation 2: 1 = d
Equation 3: 2 = a + b + c + d
Equation 4: 17 = 8a + 4b + 2c + d
Using Equation 2, substitute d = 1 into the other equations:
Equation 1: -2 = a + b + c + 1
Equation 3: 2 = a + b + c + 1
Simplify these equations further:
Equation 1: -3 = a + b + c
Equation 3: 1 = a + b + c
Combine these two equations to eliminate c:
-3 + 1 = a + b + c - (a + b + c)
-2 = 0
This indicates a contradiction, which means there is no unique polynomial that passes through all four given points.
Please double-check the given points and ensure they are accurate.