Quadratic Equation?

Question

Is there a formula to solve a quadratic equation when f(x)=0 and they give you one solution with a vertex and asking to solve for the other solution.
If not How would I solve this.

Answer 1

note
There are many ways when f(x) = o
you can use the quadratic formula as an alternative

x = [-b +/- sqrt(b^2 - 4ac)]/(2a)

If you know the vertex, you know the axis of symmetry - the x-value (x, y)

and If you know one solution then the other solution is equidistant from the axis of symmetry.

for instance, if the vertex is (1,3) then the axis of symmetry is at x = 1
if one solution is x = 4, then 4 is 3 units from the axis of symmetry. Equidistant from that is 3 units to the left of 1, which would be -2

Answer 2

If by "solution" you mean zero of the function, x-intercept of the graph, then since you have the vertex, remember the solutions are equal distances from the line of symmetry that goes through the vertex. So if the vertex is (2,-3), line of symmetry x = 2, and one solution is -1, since that's 3 left of the line of symmetry, the other solution will be 3 right at 5.

Answer 3

you are saying f(x) = y =0
say the vertex (x = 2, y = 0)
the equation is

y = ( x - 2 )^2 = 0