y = -x^2 - 6x + 11
To use the quadratic formula to find the zeroes, we need to make sure the equation is written in the form color(red)(a)x^2 + color(magenta)(b)x + color(blue)(c) = 0, which this equation is.
So we know that:
color(red)(a = -1)
color(magenta)(b = -6)
color(blue)(c = 11)
The quadratic formula is x = (-color(magenta)(b) +- sqrt(color(magenta)(b)^2 - 4color(red)(a)color(blue)(c)))/(2color(red)(a)).
Now we can plug in the values for color(red)(a), color(magenta)(b), and color(blue)(c) into the quadratic formula:
x = (-(color(magenta)(-6)) +- sqrt((color(magenta)(-6))^2 - 4(color(red)(-1))(color(blue)(11))))/(2(color(red)(-1)))
Simplify:
x = (6 +- sqrt(36 + 44))/-2
x = (6 +- sqrt(80))/-2
x = (6 +- 4sqrt5)/-2
x = -3 +- 2sqrt5
This is the same thing as:
x = -3 + 2sqrt5 and x = -3 - 2sqrt5
because +- means "plus or minus."
This means the zeros are at:
(-3 + 2sqrt5, 0) and (-3 - 2sqrt5, 0)
Hope this helps!