Question

When rewriting in the form y=a(x-h)+k, by completing the square, the relation y=-x*2+6x+12 becomes:

Answer 1

Answer:

Step-by-step explanation:

you can complete the square or use a calculator online that does it for you.

the equation is in the for y = a(x-h)^2 + k

it should be y = (x + 3)^2 + 3

Answer 2

Answer:

The correct answer is $y = - (x - 3)^{2} +21$.

Step-by-step explanation:

To solve this equation (y = $-x^{2} +6x + 12$), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve $y = -x^{2} +6x - 9 + 12$.

Then, you want to add the -9 to the other side of the equation to get $y - 9 = -x^{2} + 6x - 9 + 12$.

Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with $y - 9 = -(x^{2} -6x+9) + 12$.

Now, we use an identity in algebra that is difference of two squares identity. This says that $a^{2} -2ab +b^{2} =(a-b)^{2}$.

So, we will then factor the trinomial -$x^{2} -6x+9$ to get $-(x-3)^{2}$. Our new and updated equation is $y-9 = -(x-3)^{2} +12$.

Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us $y = -(x-3)^{2} +21$.

This is our final equation.