olve the following quadratic inequality by determining the roots, sketch the parabola in relation to the x axis and determine if the parabola is above or below

Question

solve the following quadratic inequality by determining the roots, sketch the parabola in relation to the x axis and determine if the parabola is above or below the x axis                   -x^2-x+2 less than 0

Answer 1

-x^2-x+2<0

the parabola itself is

x^2+x-2 =0

(x-1)(x+2)= 0 with x intercepts x=1 and x=-2 which are also the roots

the vertex has an x intercept = average of intercepts (1-2)/2=-1/2

y coordinate of the vertex is (-1/2)^2 -1/2+2 = 1/4 -1/2 -2 = -2.25

ertex is (-.5, -2.25) = minimum point. It's an upward opening parabola

the parabola is mostly above the x axis, but with a small portion below the x axis

the inequality -x^2 -x +2 <0

is the same as x^2 +x -2 >0

is all points below the parabola, to its right and left

sketch the parabola, then shade in the area below, right and left of the parabola

but make the parabola itself in dotted lines to indicate the inequality does not include the parabola itself