Serious Help: Quadratic Inequalities <----- dash and solid lines?

1) In a case of inequalities the graph is always solid when we have signs ≤ or ≥ (with equality) because y ≥ x^2 + x - 20 means y > x^2 + x - 20 or y = x^2 + x - 20 which is parabola itself.

When we have strict signs in inequality (>, <) the graph is always dashed and that means that equality is not accepted and parabola points are not solutions of the inequality y > x^2 + x - 20 .

2) I don't quite understand what you mean by inequality 0 > x^2 + x - 20 in this context. Here we don't have any region or any parabola cause there is no y. The solutions of this inequality lay in the interval x∈ (-5, 4) (endpoints are not in the interval because inequality sign is strict >).

0 ≥ x^2 + x - 20 solutions x ∈ [-5, 4].

y > x² + x - 20 graphs as an upward-opening shaded-inside parabola with a dotted curve because the curve is not included in the equation.

y ≥ x² + x - 20 graphs as the same parabola except it has a solid curve because the curve is included in equation.

0 > x² + x - 20

x² + x - 20 < 0

(x + 5)(x - 4) < 0

If the product of two factors is negative, then only one factor is negative.

If x + 5 < 0,

x < - 1

If x - 4 < 0,

x < 4

(- ∞ < x < - 2) U (- ∞ < x < 4)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

0 ≥ x² + x - 20

x² + x - 20 ≤ 0

(x + 5)(x - 4) ≤ 0

If x + 5 ≤ 0,

x ≤ - 5

If x - 4 ≤ 0,

x ≤ 4

(- ∞ < x ≤ - 5) U (- ∞ < x ≤ 4)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

In graphing : y>x^2+x-20, you should apply sprint line to graph y=x^2+x-20, and colour the area above the boundary of the curve. at the same time as for y>=x^2+x-20, you shoud use a superior line to graph y=x^2+x-20, and colour the area above the boundary of the curve incuding the boundary curve. For 0>x^2+x-20, you should allure to a dashed line of y=0 from x=-5 to x=4 & a superior curve of x^2+x-20=0, & colour the area between the line & the curve. For 0>=x^2+x-20, you should allure to a superior line of y=0 & a superior curve of x^2+x-20=0 & colour the area in wager- ween.