The equation provided, \( h = -16t^2 + 60t + 30 \), is a quadratic equation that opens downward because the coefficient of \( t^2 \) is negative (-16). This means the maximum height of the ball will be at the vertex of the parabola.
Let's analyze the features of the given options:
- Direction of the Curve: The graph should open downward.
- Initial Height: When \( t = 0 \), \( h = 30 \). Therefore, the graph should pass through the point (0, 30).
- Graph Characteristics: Since \( h \) represents height, it cannot be negative; thus, we should consider the relevant points where \( h \) is at least 0.
Based on these characteristics, the correct graph should show a downward-opening curve that passes through (0, 30) and does not have any positive height values significantly below that.
Among the options provided, the only graph that fulfills these criteria is:
- The one that includes a solid curve that opens downward and goes through the points (0, 30).
Specifically, the correct answer would be:
The coordinate grid has t axis labeled from negative 5 to 5 and h axis labeled from negative 60 to 90 in intervals of 15. The graph of a solid curve opens downward and goes through the points left parenthesis negative 1 comma negative 46 right parenthesis; left parenthesis 0 comma 30 right parenthesis; left parenthesis 2 comma 86 right parenthesis; and left parenthesis 4 comma 14 right parenthesis. There is shading below the curve.
This description matches the features of the quadratic and its characteristics, specifically emphasizing that it correctly represents the physical situation described.