Quartic function question?

Question

I really don't know how to do this.....

A quartic function passes throught he points (-2, 45), (-1, 48), (0, 45), (1, 48), and (2,45). Determine the equation of the function that passes through these points.

10 points to the first person who can give me the answer.

To jenh42002, why do you have to fill in 45 for all the E values? And after that, how did you "get" the values for the coefficients?

Answer 1

Ax^4 + Bx^3 + Cx^2 + Dx + E = f(x)


With (-2, 45) we get

16A - 8B + 4C - 2D + E = 45

With (-1, 48) we get

A - B + C - D + E = 48

With (0, 45) we get E = 45

With (1,48) we get A+B+C+D+E = 48

With (2,45) we get 16A + 8B + 4C + 2D + E = 45

Filling in 45 for all the Es, we have

16A - 8B + 4C - 2D = 0 --> 8A-4B+2C-D = 0
A -B+C-D+45= 48 ------> A-B+C-D = 3
A+B+C+D + 45 =48 ----> A+B+C+D = 3
16A+8B+4C+2D = 0 ----> 8A+4B+2C +D = 0

I get A = -1, C= 4, B = 0, D = 0, so

-x^4 + 4x^2 + 45 = f(x)

Answer 2

y = ax^4+bx^2+45
45 = 16a+4b+45 => 4a+b = 0......(1)
48 = a+b+45 => a+b = 3......(2)
(1)-(2), 3a = -3
a = -1
b = 4
y = -x^4+4x^2+45
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Ideas: The quartic function is an even function.

Answer 3

P(x) = x^4 - 4x^3 + 3x^2 + 4x - 4 First, locate the 1st by-product or P'(x) 4x^3 - 12x^2 + 6x + 4 (divide the entire term through 2) 2x^3 - 6x^2 + 3x + 2 then do the exchange branch technique 2 - 6 + 3 + 2 l_2_l 4 -4 -2 -------------------- 2 - 2 -one million 0 2x^2 - 2x - one million then use the quadritic formulation the solutions must be 2, -0. 37, and1.37 in case you will use the quadratic formulation you will possibly get an answer with an intensive.

Answer 4

(x,y) = (+1,+3)