I am having trouble with this problem. I have done it several times and come up with two different answers. Can someone tell me what I am doing wrong?
Write the quadratic function in the form a(x-h)^2+k
y=x^2-2x-9
(x^2-2x)-9
(x^2+2x+1-1)-9
(x^2+2x+1)
answers
(x+1)^2 or x^2-2x-9=y
I believe you are missing k. Remember y = x^2-2x-9 and y = a(x-h)^2+k. What you have gotten for y is (x+1)^2. If you expand it, you'll see that it is x^+2x+1 which is not equal to x^2-2x-9. From your work which I believe is mostly correct but you made a tiny mistake. You pulled out -9 and -1, -10, from the original equation. That should be what you're missing. Even though you pulled them out they don't disappear into thin air ;/.
So.....
from your answer I need to add a -10 to (x+1)^2+2x+-10?
It seems like you're trying to rewrite the quadratic function y=x^2-2x-9 in the form a(x-h)^2+k. Let's go through the steps to see where the discrepancy might be.
To rewrite y=x^2-2x-9 in the form a(x-h)^2+k, we need to complete the square. Here's how:
1. Start with the original quadratic function: y=x^2-2x-9.
2. Group the terms involving x: (x^2-2x)-9.
3. To complete the square, take half of the coefficient of x, square it, and add it inside the parentheses. In this case, half of -2 is -1, and squared is 1. So, we rewrite it as: (x^2-2x+1)-1-9.
4. Simplify the expression inside the parentheses: (x^2-2x+1)-10.
5. The expression inside the parentheses (x^2-2x+1) is a perfect square trinomial, which can be written as (x-1)^2.
6. Rewrite the entire expression: (x-1)^2-10.
So, the correct answer is y = (x-1)^2-10.
It appears that in one of your attempts, you mistakenly added 1 instead of subtracting 1 when completing the square. That led to an incorrect answer of (x+1)^2. Always make sure to follow the proper steps of completing the square to avoid errors.