How do you find the roots, real and imaginary, of #y= -2(x-3)^2+(-x-2)^2 # using the quadratic formula?
Check below for my work!
You need to put it this in a form that's usable with the quadratic formula. Generally you want an equation in the form of
Let's work with the equation a bit. To start, we have two binomials to the power of two. We can expand these with multiplication.
Great! Now we're left with
Now we can multiply the first polynomial by
That leaves us with
Now we simply combine like terms.
Pulling from our simplified polynomial, we can plug these values into the quadratic formula.
Finally, we solve!
*I'm splitting the
Since these can't be simplified any further, these are the real roots. There are no imaginary roots.