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### 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:

or
Now substitute that value of x into the original equation and
solve for the

y-coordinate,substituting back
in.

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