Thanks to Geno, Melody, Heureka and Guest !!!
Here's an algebraic solution.......
As the Guest pointed out.....this will be a 4th degree polynomial in the form
ax^4 + bx^3 + cx^2 + dx + e
Since (0, -3) is on the graph, then e = - 3
We can first solve for a and c
So we have that
a(-2)^4 + b(-2)^3 + c(-2)^2 + d(-2) - 3 = 29
a(2)^4 + b(2)^3 + c(2)^2 + d(2) - 3 = 29
Adding these, we have that
32a + 8c - 6 = 58
32a + 8c = 64
4a + c = 8 (1)
And we have that
a(1)^4 + b(1)^3 + c(1)^2 + d(1) - 3 = -1
a(-1)^4 + b(-1)^3 + c(-1)^2 + d(-1) - 3 = -1
Adding these we get that
2a + 2c = 4
a + c = 2 (2)
Subtract (2) from (1)
3a = 6 ⇒ a = 2
And 2 + c = 2 ⇒ c = 0
And we have that
2 (1)^4 + b(1)^3 + d(1) - 3 = -1
2(-1)^4 + b(-1)^3 + d(-1) - 3 = - 1
Subtract these
2b + 2d = 0
b + d = 0 (3)
And
2(2)^4 + b(2)^3 + d(2) - 3 = 29
2(-2)^4 + b(-2)^3 + d(-2) - 3 = 29
Subtract these
16b + 4d = 0
4b + d = 0 (4)
Subtract (3) from (4)
3b = 0
b = 0
And b + d = 0 ⇒ 0 + d = 0 ⇒ d = 0
So......the function is
2x^4 - 3
