Question

find the equation of the cubic equation show graph passes through the points (3,0) and (1,4) and is tangent to the axis at the origin???
I honestly cannot figure this out and can you explain the graph to me too?

Answer 1

Since it is tangent at the origin, there has to be double root at (0,0). Also (3,0) is an x-intercept

so we can let the equation be
y = ax^2(x-3)
but (1,4) lies on it
4 = a(1)(-2)
a = -2

function is

f(x) = -2x^2(x-3)
expand if needed

Proof:
http://www.wolframalpha.com/input/?i=plot+-2x%5E2%28x-3%29+%2C+x+%3D+-2%2C+x+%3D+4