The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
<h3>What inequality represents the figure</h3>
In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the <em>quadratic</em> equation of the parabola:
f(x) = a · (x + 1) · (x - 9)
- 125 = a · (4 + 1) · (4 - 9)
- 125 = a · 5 · (- 5)
- 125 = - 25 · a
a = - 5
f(x) = 5 · (x + 1) · (x - 9)
f(x) = 5 · (x² - 8 · x - 9)
f(x) = 5 · x² - 40 · x - 45
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
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