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In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the
In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?
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Q1
In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?
The graph opens upwards.
The graph opens downwards.
The graph is a straight line.
The graph is a constant function.
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When a > 0 in a quadratic function, the graph opens upwards, indicating that the vertex is the minimum point.
Questions & Step-by-step Solutions
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Q
Q: In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?
Solution:
When a > 0 in a quadratic function, the graph opens upwards, indicating that the vertex is the minimum point.
Steps: 5
Show Steps
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.
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