In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the

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Question: In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?

Options:

Correct Answer: The graph opens upwards.

Solution:

When a > 0 in a quadratic function, the graph opens upwards, indicating that the vertex is the minimum point.

In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?

In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?

Step 1: Identify the function type. The function is a quadratic function of the form f(x) = ax^2 + bx + c.
Step 2: Look at the coefficient 'a'. In this case, we know that a > 0.
Step 3: Understand what 'a > 0' means. When 'a' is positive, it affects the shape of the graph.
Step 4: Determine the direction of the graph. A positive 'a' means the graph opens upwards.
Step 5: Identify the vertex of the graph. Since the graph opens upwards, the vertex is the lowest point on the graph.

Quadratic Functions – Understanding the general form of a quadratic function and how the coefficient 'a' affects the graph's direction.
Graph Behavior – Recognizing how the sign of 'a' determines whether the parabola opens upwards or downwards.
Vertex of a Parabola – Identifying the vertex as the minimum or maximum point based on the direction of the parabola.