A quartic graph has the following coordinates:

(-4,0),(-2,0),(0,0),(1,0)
find the equation in expanded form.

You have listed the 4 roots, so

y = a(x+4)(x+2)(x)(x-1)
= a(x^4+5x^3+2x^2-8x)

To find the equation of a quartic graph from its coordinates, we can use the fact that the general form of a quartic equation is:

y = ax^4 + bx^3 + cx^2 + dx + e

Since we know that the graph passes through the given points, we can substitute the coordinates into this equation to form a system of equations.

Let's substitute the x and y values from each point:

For the point (-4, 0):
0 = a(-4)^4 + b(-4)^3 + c(-4)^2 + d(-4) + e

Simplifying this equation, we get:
0 = 256a - 64b + 16c - 4d + e

Next, for the point (-2, 0):
0 = a(-2)^4 + b(-2)^3 + c(-2)^2 + d(-2) + e

Simplifying further, we get:
0 = 16a - 8b + 4c - 2d + e

Now, for the point (0, 0):
0 = a(0)^4 + b(0)^3 + c(0)^2 + d(0) + e

This equation simplifies to:
0 = e

And finally, for the point (1, 0):
0 = a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e

Simplifying, we have:
0 = a + b + c + d + e

So, we have a system of equations:

256a - 64b + 16c - 4d + e = 0
16a - 8b + 4c - 2d + e = 0
e = 0
a + b + c + d + e = 0

To solve this system, we can use various methods such as substitution or elimination. However, since the last equation tells us that e = 0, we can substitute e = 0 into the other equations to simplify the calculations.

Substituting e = 0 into the first two equations, we get:

256a - 64b + 16c - 4d = 0
16a - 8b + 4c - 2d = 0

Now, we have two equations with four variables (a, b, c, d), so we need to use additional information to find a unique solution. Since no additional information is given, we cannot determine the specific values of a, b, c, and d.

However, we can write the equation of the quartic graph in expanded form by substituting arbitrary values for a, b, c, and d. For instance, assuming a = 1, b = 2, c = 3, and d = 4, the equation in expanded form would be:

y = x^4 + 2x^3 + 3x^2 + 4x

Please note that this specific equation is just an example, and without additional information, we cannot uniquely determine the values of a, b, c, and d.