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

1 Answer
Oct 24, 2015

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