Quadratic Domain and Range

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•
Mathematics
•
9th - 10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the domain of a quadratic function?
Back
The domain of a quadratic function is all real numbers, represented as (-∞, ∞).
2.
FLASHCARD QUESTION
Front
What is the range of a quadratic function that opens upwards?
Back
The range is all real numbers greater than or equal to the minimum value of the function, typically expressed as [k, ∞) where k is the minimum value.
3.
FLASHCARD QUESTION
Front
What is the range of a quadratic function that opens downwards?
Back
The range is all real numbers less than or equal to the maximum value of the function, typically expressed as (-∞, k] where k is the maximum value.
4.
FLASHCARD QUESTION
Front
How do you find the vertex of a quadratic function in standard form?
Back
The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.
5.
FLASHCARD QUESTION
Front
What are x-intercepts of a quadratic function?
Back
The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation f(x) = 0.
6.
FLASHCARD QUESTION
Front
What is the significance of the discriminant in a quadratic equation?
Back
The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.
7.
FLASHCARD QUESTION
Front
What does it mean for a quadratic function to be in vertex form?
Back
Vertex form is expressed as f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.
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