Artem :
You’re wrong. We need to analyze each graph labeled F, G, H, and J. A quadratic function typically has a parabolic shape, and its range depends on the vertex and the direction it opens. The range refers to all possible y-values the function can take. Since the range must be all real numbers greater than or equal to 3, the lowest y-value of the parabola should be 3, and the parabola should extend upward to infinity if it opens upward, or downward to negative infinity if it opens downward, but still satisfy the range condition.
Let’s start by recalling the general form of a quadratic function, which is y = ax^2 + bx + c. The coefficient a determines the direction the parabola opens: if a is positive, it opens upward, and if a is negative, it opens downward. The vertex of the parabola is the turning point, and for a parabola opening upward, the range is all y-values greater than or equal to the y-coordinate of the vertex. For a parabola opening downward, the range is all y-values less than or equal to the y-coordinate of the vertex.
Given the range requirement of y being greater than or equal to 3, the vertex’s y-coordinate should be 3, and the parabola should open upward to include all values above 3. If the parabola opens downward, the range would be all values less than or equal to the vertex’s y-coordinate, which would not satisfy the condition unless the vertex’s y-coordinate were adjusted, but we’ll check each graph to confirm.
Now, let’s examine graph F. The parabola opens downward, with its vertex appearing to be at the point (0, 4) since the highest point on the graph is at y = 4 on the y-axis. Since it opens downward, the range includes all y-values less than or equal to 4, extending downward to negative infinity. This does not match our requirement, as the range includes values below 3, such as 2, 1, and negative numbers.
Next, let’s look at graph G. This parabola also opens downward, with its vertex at (0, 5), the highest point on the graph. The range here is all y-values less than or equal to 5, again extending downward to negative infinity. The answer is H.
2025-05-23 04:30:18