Aparabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.

which could be the equation of the parabola?

A parabola is the set of all points that lies on a plane and are equidistant from  a fixed line called the directrix and a fixed point called focus, that doesn't lies on the line. If the  vertex is at the origin and the directrix crosses the negative part of the y-axis, then the equation takes the following forms:

Where the focus lies on the axis (directed distance) from the vertex.

The representation of this problem is shown below. As you can see, the vertex lies on the origin while the directrix crosses the negative part of the y-axis.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source