Question: Review the graph of \( x + 3.5 < \frac{1}{10}(y - 2)^2 \). Which justification can be used to…

Review the graph of \( x + 3.5 < \frac{1}{10}(y - 2)^2 \).

Which justification can be used to demonstrate the graph is correct?

Boundary values are included as part of the solution set.

Shading is to the left because \((0, 0)\) does not satisfy the inequality.

The coefficient of the \(y^2\) term is a fraction, so the parabola opens to the right.

The positive coefficient \(\frac{1}{10}\) indicates the parabola opens up.

Solution

The problem asks for a justification of the graph of the inequality \( z = 3.5 < \frac{1}{10}(y - 2)^2 \). The given inequality represents a parabola. Let’s analyze the options for the correct justification: 1. Boundary values are included as part of the solution set. This is incorrect because the inequality is strict (\(<\)), so boundary values are not included. 2. Shading is to the left because \((0, 0)\) does not satisfy the inequality. This might be plausible, but it depends on further checking. 3. The coefficient of the \(y^2\) term is a fraction, so the parabola opens to the right. This is incorrect. The orientation of the parabola depends on the sign, not whether the coefficient is a fraction. 4. The positive coefficient \(\frac{1}{10}\) indicates the parabola opens up. This is correct. A positive coefficient for the squared term indicates the parabola opens upward or to the right in a horizontal situation. The correct justification is: The positive coefficient \(\frac{1}{10}\) indicates the parabola opens up.