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Questions and Answers
What is the axis of symmetry in a quadratic function?
What is the axis of symmetry in a quadratic function?
- A diagonal line that intersects the x-axis
- A horizontal line through the vertex
- A vertical line that passes through the vertex (correct)
- A line that represents the maximum value of the function
Which statement describes how to find the maximum or minimum value of a quadratic function?
Which statement describes how to find the maximum or minimum value of a quadratic function?
- It is found by evaluating the function at the x-intercept
- It is located at the vertex of the parabola (correct)
- The maximum or minimum is determined by the domain of the function
- The maximum or minimum occurs at the y-intercept
What is the relationship between the direction of opening and the maximum or minimum value in a quadratic function?
What is the relationship between the direction of opening and the maximum or minimum value in a quadratic function?
- A parabola that opens upwards has a maximum value
- The direction of opening does not affect the vertex
- A parabola that opens upwards has a minimum value (correct)
- A parabola that opens downwards has a minimum value
What characteristics define the range of a quadratic function that opens downward?
What characteristics define the range of a quadratic function that opens downward?
How can one identify the x-intercepts of a quadratic function?
How can one identify the x-intercepts of a quadratic function?
Flashcards
Direction of Opening
Direction of Opening
Describes whether a parabola opens upwards or downwards.
Vertex
Vertex
The point where the parabola changes direction.
Axis of Symmetry
Axis of Symmetry
A vertical line passing through the vertex.
Minimum
Minimum
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Maximum
Maximum
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Study Notes
Properties of Quadratics Part 2
- Parabola Parts: A parabola is a U-shaped graph. The turning point is called the vertex. If the parabola opens upward, the vertex is a minimum point; if it opens downward, it is a maximum point.
- Minimum/Maximum Value: The y-value of the vertex is the minimum or maximum value of the quadratic function.
- Domain: The set of all possible x-values for a quadratic function. Quadratic functions have a domain of all real numbers.
- Range: The set of all possible y-values for a quadratic function. The range is affected by the minimum or maximum value of the quadratic function.
- If the parabola opens upward (minimum), the range is from the y-value of the vertex to positive infinity.
- If the parabola opens downward (maximum), the range is from negative infinity to the y-value of the vertex
Example Problems
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Example 1: For the function f(x) = (x + 3)² - 4
- Direction of opening: Up
- Vertex: (-3, -4)
- Axis of symmetry: x = -3
- Minimum value: -4
- Domain: (-∞, ∞)
- Range: [-4, ∞)
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Example 2: For the function f(x) = -x² - x + 6
- Direction of opening: Down
- Vertex: (-0.5, 6.25)
- Axis of symmetry: x = -0.5
- Maximum value: 6.25
- Domain: (-∞, ∞)
- Range: (-∞, 6.25]
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