Question

How many points do you need to determine the equation of a parabola?

Answer 1

2: the vertex and another point

Explanation:

the vertex gives the values `(h,k)`
another point gives `(x,y)`
these can be plugged into vertex form, `y=a(x-h)^2 +k`

to get the equation of a parabola in standard form:
once the four values are plugged into vertex form, the equation can be solved for the variable `a`

`b` can then be found using `x=((-b)/(2a))`

to find `c`, plug in the `a` and `b` values into `y=ax^2+bx+c` as well as the point from before (for `x` and `y`) and solve it

finally, plug the `a`, `b`, and `c` values into `y=ax^2+bx+c` and you have your equation in standard form

there are probably other ways to do this, but overall, a minimum of 2 points is needed