The standard form of the equation of a parabola is $x=y^2-4y+20$ . What is the vertex form of the equation?

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Answer 1 · 2016-06-14T05:06:58

Solution

The standard forms of the equation of the parabola are of $y^2=4ax$ and $x^2=4ay$ .

Here we have
$y^2-4y+16=x$

This is a shifted parabola of $y^2=4ax$ form.

Make the $LHS$ to the whole square part

Then,

$y^2-4y+4+12 =x$
$(y-2)^2=x-12$
Compare it with $RHS$

So we have
$(y-2)^2=4*1/4*(x-12)$

The standard form of the equation of a parabola is x=y^2-4y+20x=y^2-4y+20. What is the vertex form of the equation?