Question

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Explanation:

Analyze the given inequality

Using the Quadratic Modeling knowledge point

$$ d \le \frac{1}{5}w^2 $$

where \(d\) is the dosage in milligrams (vertical axis) and \(w\) is the dog's weight in pounds (horizontal axis).

Identify the boundary curve

The boundary curve is the parabola:

$$ d = \frac{1}{5}w^2 = 0.2w^2 $$

Let's calculate key points on this boundary curve:

• For \(w = 0\): \(d = 0\)
• For \(w = 10\): \(d = 0.2 \times 100 = 20\)
• For \(w = 20\): \(d = 0.2 \times 400 = 80\)
• For \(w = 30\): \(d = 0.2 \times 900 = 180\)
• For \(w = 40\): \(d = 0.2 \times 1600 = 320\)

Determine the shaded region

The inequality is \(d \le \frac{1}{5}w^2\).
For any given weight \(w\), the dosage \(d\) must be less than or equal to the value on the curve.
This means the shaded region must be below the boundary curve.

Evaluate the options

• Option A: The boundary curve passes through \((20, 80)\) and \((40, 320)\) (or similar scale), but the shaded region is above the curve (the upper-left region is shaded). This represents \(d \ge \frac{1}{5}w^2\).
• Option B: The boundary curve is the same parabola, and the shaded region is below and to the right of the curve. This represents \(d \le \frac{1}{5}w^2\).
• Option C: The curve shown is different or has incorrect shading/curvature.

Therefore, Option B correctly displays the inequality \(d \le \frac{1}{5}w^2\).

Answer:

• (A) Parabola curve with shading above the curve
• (B) Parabola curve with shading below the curve (Correct answer)
• (C) Incorrect curve or shading