What is the equation of the parabola that has a vertex at $(4, 2)$ and passes through point $(6,34)$ ?

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Answer 1 · 2018-04-25T11:22:34

$y = 8(x-4)^2+2$

When the parabola has a vertex at $(4,2)$ its equation looks like $y= a(x-4)^2+2$ and we plug in $(6,34)$ to find $a$ :

$34=a(6-4)^2+2$

$32=4a$

$a=8$

So we get

$y = 8(x-4)^2+2$

We could expand this into standard form, but at this point we've answered the question so let's stop.

Check: The vertex is correct by construction.

$8(6-4)^2 +2 = 8(4)+2 = 34 quad sqrt$

What is the equation of the parabola that has a vertex at (4, 2) (4, 2) and passes through point (6,34) (6,34) ?