which equation represents y=-x^2+4x-1 in vertex form

Question

mathmale · Answer

Welcome to OpenStudy!  Glad you're here!
You have a quadratic equation here.  Your task is to re-write it so that the coordinates of the vertex of this parabola are obvious.

mathmale · Answer

The correct form of the equation of a quadratic for that purpose is$$y=a(x-h)^2+k$$

mathmale · Answer

So, basically, you need to re-write the given equation in that form.  How would you do that?

mathmale · Answer

$$y=-x^2+4x-1 \rightarrow y=a(x-h)^2+k$$

mathmale · Answer

Hint:  your " a " is going to be negative.

mathmale · Answer

@johnweldon1993:  Thanks for your input, John.  But wouldn't there be a negative coefficient, " a ", in this picture?  Please, do your best to guide maddierawr through the solution of this problem without doing the actual work for her, OK?  

@maddierawr?  Where are we?  What's our goal?  What's the next step towards identifying the coordinates of the vertex of this parabola?

anonymous · Answer

Just complete the square and you are done.

anonymous · Answer

$$
y=-x^2+4 x-1=-\left(x^2-4 x+4-4\right)-1=\-\left(x^2-4
   x+4\right)+4-1=-(x-2)^2 +3

$$

mathmale · Answer

Note how eliassaab has taken that negative sign out of the original expression, which is absolutely the correct thing to do.
@maddierawr :  You've gotten a lot of info here already; hope it's not overwhelming.  Please let us know where you are at this point:  what do you understand, and what do you need to know to finish solving this problem?