How do you write the vertex form equation of the parabola y=-x^2+2x+3?

1 Answer
Jun 4, 2017

Complete the square.

Explanation:

For y=-x^2 + 2x +3, take out the factor of -1 to make the x^2 coefficient +1.

:. y=-(x^2-2x-3)

Now, complete the square. Divide the x coefficient by 2 and square it, adding it and subtracting it.

:. y=-(x^2-2x+1-1-3)
:. y=-((x-1)^2-4)
:. y=-(x-1)^2 + 4

This is now in turning-point form; simply read off the coordinates of your vertex, which is at (1,-4). Remember that this is a local maximum. Of course, the original equation factorises quite easily, so for sketching purposes, make y=-(x-3)(x+1) to get your x-intercepts; the y-intercept is, of course, just the constant term in the original equation.