The general equation of a parabola is:. We know by the shape of the parabola that the tangent line at the vertex will be horizontal, or slope=0.
We can find the equation for the slope of the tangent line to our parabola taking the derivative . When we set the resultant equation to zero and solve for x, we will get the x-coordinate of the vertex:
Now substitute that value of x into the original equation and solve for the
y-coordinate,substituting back in.