Locus of Vertices of Parabola

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.

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