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In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine?

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Question: In a function f(x) = ax^2 + bx + c, what does the coefficient \'a\' determine?

Options:

  1. The direction of the parabola\'s opening.
  2. The y-intercept of the graph.
  3. The slope of the graph.
  4. The x-intercepts of the graph.

Correct Answer: The direction of the parabola\'s opening.

Solution: 

The coefficient \'a\' in a quadratic function determines whether the parabola opens upwards (a > 0) or downwards (a < 0).

In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine?

Practice Questions

Q1
In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine?
  1. The direction of the parabola's opening.
  2. The y-intercept of the graph.
  3. The slope of the graph.
  4. The x-intercepts of the graph.

Questions & Step-by-Step Solutions

In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine?
  • Step 1: Identify the function f(x) = ax^2 + bx + c.
  • Step 2: Look at the coefficient 'a' in front of x^2.
  • Step 3: Determine if 'a' is greater than 0 (a > 0) or less than 0 (a < 0).
  • Step 4: If 'a' is greater than 0, the parabola opens upwards.
  • Step 5: If 'a' is less than 0, the parabola opens downwards.
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