(−∞,−3) (2,+∞)
Step-by-step explanation:
graph the parabola
y=−x2−x+6
and consider which parts are less than zero, that is below the x-axis finding the x and y intercepts
let x = 0, in the equation for y-intercept
let y = 0, in the equation for x-intercepts
x=0→ y=6←
y-intercept
y=0→ −x2−x+6=0
multiply through by - 1
⇒ x2+x−6=0
the factors which multiply to give - 6 and sum to + 1 are + 3 and - 2
⇒(x+3)(x−2)=0
⇒x=−3 or x=2←
x-intercepts
obtaining the shape of the parabola
if a>0
then minimum if a < 0
then maximum for y =−x2−x+6xa<0
we can now graph the parabola
graph{-x^2-x+6 [-10, 10, -5, 5]}
x<−3 or x>2
are the parts below the x-axis
in interval notation
(−∞,−3)∪(2,+∞)