I don't understand the parabola definition and what is the algebraic equation?
thank you:)

I can give you the parabola but you will have to fill out the algebraic equation yourself, which isn't all that difficult

a parabola is a curve in the Cartesian plane defined by an irreducible equation of the form

A x^2 + B xy + C y^2 + D x + E y + F = 0 \,

such that B^2 = 4 AC \, where all of the coefficients are real, where A \not= 0 \, or C \not= 0 \, and where more than one solution, defining a pair of points (x, y) on the parabola, exists. That the equation is irreducible means it does not factor as a product of two not necessarily distinct linear equations.

Is it y=4x^2?

Is it y=4x^2?

y = 4x^2 is certainly a parabola.

The general form for a parabola is:

y = Ax^2 + Bx + C.

Here if A >0, the parabola opens upward, and if A is negative it opens downward. For the example you gave y = 4x^2, the value of A is 4, B is 0 and C is 0. So this parabola opens upward.

If you can convert this to the form y-k =a(x-h)^2, then the vertex is at the point (h,k). For the example case of y = 4x^2, this can convert to:
y-0 = 4(x-0)^2, so this tells you the vertex is at (0,0).