what is x^2-6x+11 in y=(x-h)^2+k?

Answer 1

Hey there!

Here's the answer.

y=x^2-6x+11 --> Write the problem.
y=(x^2-6x+9)+2 --> Replace 11 with 9+2.
y=(x-3)^2+2 Factor out x^2-6x+9, by using the formula (a-b)^2=a^2-2ab+b^2.

So the equation is y=(x-3)^2+2, with (3,2) being the vertex of the parabola.

Hope it helps!

Answer 2

Ms KK, there is a technique call "completing the square" which can be used to find the roots of quadratics. This is what you are doing here. Although we don't have a perfect square, we are close, since x^2-6x+9 is a perfect square (x-3)^2. So we can rewrite the quadratic as (x-3)^2+2. Thus h=3 and k=2.