How to write an equation and solve this?

Question

Find a formula for a degree-four polynomial function (quartic) that has the graph below. If you would like to enlarge the graph or make numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser’s zoom capabilities. On a PC this is usually ctrl shift + (and zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple -).

Answer 1

(x-1)(x+1)(x+4)^2

=(x^2-1)(x+4)^2

= (x^2-1)(x^2 +8x +16)

= x^4+8x^3 +15x^2 -16

take each x intercept, change its sign, stick an x in front of it, multiply the factors together. for an x intercept where the curve doesn't intersect but just touches the x axis, that's a zero with multiplicity two, so raise it to an exponent of 2. -4 becomes x+4 than (x+4)^2

Answer 2

(x+4)² (x+1) (x-1)

Roots are 1, -1 and double root -4.