Question

What is the vertex of `y= (x+1)^2-2x-4`?

Answer 1

Vertex form`" "y=(x+0)^2-3`

So the vertex is at `(x,y)->(0,-3)`

This is the same as `y=x^2-3`

Explanation:

There is an inherent `bx` term within `(x+1)^2`. Normally you would expect all of `bx` terms to be within the brackets. One is not! Consequently the brackets have to be expanded so that the excluded term of `-2x` can be incorporated with the term (hidden) in the brackets.

Expanding the brackets `y= (x^2+2x+1) -2x-4`

Combining terms:`" "y=x^2+0x-3`

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`color(blue)("Determine the vertex form")`

Standard form:`" "y=ax^2+bx+c" "` in your case `a=1`

Vertex form:`" "y=a(x+b/(2a))^2+c -a(b/(2a))^2`

But `b/(2a)=0" "` so `" "-a(b/(2a))^2=0`

`y=(x+0)^2-3" " ->" " y=x^2-3`