If the graph of a function is a parabola opening upwards, which of the following

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Question: If the graph of a function is a parabola opening upwards, which of the following can be inferred about the function?

Options:

Correct Answer: The function has a minimum value.

Solution:

A parabola that opens upwards indicates that the function has a minimum value at its vertex.

If the graph of a function is a parabola opening upwards, which of the following can be inferred about the function?

If the graph of a function is a parabola opening upwards, which of the following can be inferred about the function?

Step 1: Understand what a parabola is. A parabola is a U-shaped curve that can open either upwards or downwards.
Step 2: Identify the direction of the parabola. If it opens upwards, it means the arms of the U shape go up.
Step 3: Recognize that the vertex is the highest or lowest point of the parabola. For an upward-opening parabola, the vertex is the lowest point.
Step 4: Conclude that since the vertex is the lowest point, the function has a minimum value at this vertex.

Parabola Orientation – A parabola that opens upwards indicates that the function has a minimum value at its vertex.
Vertex of a Parabola – The vertex of an upward-opening parabola represents the minimum point of the function.
Quadratic Functions – The general form of a quadratic function is f(x) = ax^2 + bx + c, where a > 0 indicates an upward-opening parabola.