Question

How do you find the zeros, real and imaginary, of `y=-x^2-2x+9` using the quadratic formula?

Answer 1

The Quadratic Formula is very useful in finding the roots of an equation. The formula is:
`(-b+-sqrt(b^2-4*a*c))/(2*a)`
Where `a, b` and `c` come from `a^2x+bx+c`

So, in our equation (`y=-x^2-2x+9`), `color(purple)(a)=color(purple)(-1)`, `color(green)(b)=color(green)(-2)`, and `color(red)(c)=color(red)(9)`

Thus, our equation is:
`(-(color(green)(-2))+-sqrt((color(green)(-2))^2-4*(color(purple)(-1))*(color(red)(9))))/(2*color(purple)(-1))`
`(2+-sqrt(4--36))/(-2)`
`(2+-sqrt40)/-2`
`(2+-2sqrt(10))/-2`
`(cancel(2)(1+-sqrt10))/cancel(-2)`
`1+-sqrt10`

Thus, `x=1+-sqrt10`, which is about `4.162` and `2.162`. Those are the roots of `y=-x^2-2x+9`)