Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros –3.5 and 11.5 and includes the point (8.5, –54) on the boundary?

Answers

The inequality is represented by the polynomial y ≥ 3.6 · (x – 11.5) · (x + 3.5).

What is the expression of the quadratic inequality?

Herein we must derive the quadraticexpression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadraticequation by solving this system of linearequations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a – 3.5 · b + c = 0 (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0 (2)

(x₃, y₃) = (8.5, – 54)

72.25 · a + 8.5 · b + c = – 54 (3)

The solution of the system is a = 3.6, b = – 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² – 54 · x + 144.9, whose factoredform is determined by the quadratic formula:

inequalityis represented by thepolynomialy ≥ 3.6 · (x – 11.5) · (x + 3.5).## What is the expression of the quadratic inequality?

quadraticexpressionwithin an inequality of the y ≥ f(x) based on its tworootsand a knownpointon thecurve. We can find thecoefficientsof thequadraticequationby solving thissystemoflinearequations:(x₁, y₁) = (- 3.5, 0)(1)(x₂, y₂) = (11.5, 0)(2)(x₃, y₃) = (8.5, – 54)(3)systemis a = 3.6, b = – 54, c = 144.9. Thus, theinequalityis represented by thepolynomialy ≥ 3.6 · x² – 54 · x + 144.9, whosefactoredformis determined by thequadratic formula:inequalities: https://brainly.com/question/20383699