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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?
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?
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?
What characteristics define the range of a quadratic function that opens downward?
What characteristics define the range of a quadratic function that opens downward?
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How can one identify the x-intercepts of a quadratic function?
How can one identify the x-intercepts of a quadratic function?
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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.
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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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Description
Explore the characteristics of quadratic functions in this quiz on the properties of parabolas. Learn about vertexes, minimum and maximum values, domain, and range. Test your understanding with example problems and enhance your algebra skills.
