Question

x^2-6x+8=y
find the vertex of the parabola by complete the square.

Answer 1

Do you need help with completing the square, vertex of the parabola, or both?

Answer 2

both

Answer 3

OK, give me one second, it's been a couple of years for this

Answer 4

ok

Answer 5

first coordinate of the vertex is \(-\frac{b}{2a}\) in your case it is \(-\frac{-6}{2\times 1}=3\)
second coordinate is what you get when you replace \(x\) by \(3\)

Answer 6

To complete the square, you must first substitute 0 for y. Your equation is then x^2-6x=-8. Second, take half of the 'b' term (AKA -6x), which is -3, and then square it, which is 9.

Answer 7

@nickjesus3 question is only for the vertex, not to solve equal zero by completing the square
first coordinate of the vertex is 3, second is what you get when you replace \(x\) by \(3\) namely \(3^2-6\times 3+8=9-18+8=-1\) so vertex is \((3,-1)\)

Answer 8

@Satellite, I could be reading the question wrong, but it said find the vertex by completing the square

Answer 9

But it looks like you have the answer anyways.

Answer 10

ah i see you are right it says find the vertex by completing the square. but in this case to complete the square you don't add and subtract to both sides, unless you are finding the zeros. you have to work on one side
on the other hand, once you have the vertex you can write it in "vertex form" i.e. cheat your math teacher.
since the vertex is \((3,-1)\) vertex form is
\[y=(x-3)^2-1\] in other words you can complete the square without doing all the work