Question

What is the vertex form of `y = x^2 -14x + 16`?

Answer 1

`y=(x-7)^2-33`

Explanation:

First find the vertex using the formula
`x=(-b)/"2a"`

a=1
b=-14
c=16

`x=(-(-14))/"2(1)"` This simplifies to `x=14/"2"` which is 7.
so `x=7`

So on now that we have x we can find y.

`y=x^2-14x+16`
`y=(7)^2-14(7)+16`
`y=-33`

`Vertex = (7,-33)` where h=7 and k=-33

We now finally enter this into vertex form which is,
`y=a(x-h)^2+k`

x and y in the "vertex form" are not associated with the values we found earlier.

`y=1(x-7)^2+(-33)`
`y=(x-7)^2-33`