Question

which graph best represents a quadratic function with a range of all real numbers greater than or equal to 3? 4.

Explanation:

Step1: Recall Quadratic Function Range

A quadratic function \( y = ax^2 + bx + c \) has a parabola graph. If \( a>0 \), it opens upward, and the range is \( y \geq k \) (where \( k \) is the y - coordinate of the vertex). If \( a < 0 \), it opens downward, and the range is \( y\leq k \). The problem requires a range of all real numbers greater than or equal to 3, so the parabola should open upward ( \( a>0 \)) and the vertex's y - coordinate should be 3.

Step2: Analyze Each Graph

• Graph F: Opens downward (since it has a maximum point), so its range is \( y\leq k \), not \( y\geq3 \). Eliminate F.
• Graph G: Opens downward (has a maximum point), so its range is \( y\leq k \), not \( y\geq3 \). Eliminate G.
• Graph H: Opens upward, but let's check the vertex's y - coordinate. From the graph, the vertex seems to be below \( y = 3 \).
• Graph J: Opens upward, and the vertex's y - coordinate appears to be 3 (or at least in line with the range \( y\geq3 \)).

Answer:

J. The graph labeled J