How do you solve quadratic inequality, graph, and write in interval notation # -x^2 - x + 6 <0#?

1 Answer
Aug 3, 2017

Answer:

#(-oo,-3)uu(2,+oo)#

Explanation:

#"graph the parabola "y=-x^2-x+6#
#"and consider which parts are less than zero, that is below"#
#"the x-axis"#

#color(blue)"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=0toy=6larrcolor(red)"y-intercept"#

#y=0to-x^2-x+6=0#

#"multiply through by - 1"#

#rArrx^2+x-6=0#

#"the factors which multiply to give - 6 and sum to + 1"#
#"are + 3 and - 2"#

#rArr(x+3)(x-2)=0#

#rArrx=-3" or "x=2larrcolor(red)" x-intercepts"#

#color(blue)"obtaining the shape of the parabola"#

#• " if "a>0" then minimum " uuu#

#• " if "a<0" then maximum " nnn#

#"for "y=-x^2-x+6color(white)(x)a<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" (-oo,-3)uu(2,+oo)#