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

1 Answer
Rachel
Apr 14, 2017

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)

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