Quadratic Equations with Real or Complex Solutions

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•
Mathematics
•
9th - 11th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is used to find the solutions (or roots) of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).
2.
FLASHCARD QUESTION
Front
What are the zeros of a quadratic function?
Back
The zeros of a quadratic function are the values of x for which the function equals zero. They can be found by factoring the equation or using the quadratic formula.
3.
FLASHCARD QUESTION
Front
What shape does the graph of a quadratic function take?
Back
The graph of a quadratic function is called a parabola.
4.
FLASHCARD QUESTION
Front
What is the discriminant in a quadratic equation?
Back
The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, and it determines the nature of the roots.
5.
FLASHCARD QUESTION
Front
What does the discriminant tell us about the roots of a quadratic equation?
Back
If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if it is negative, there are two complex roots.
6.
FLASHCARD QUESTION
Front
What is the standard form of a quadratic equation?
Back
The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.
7.
FLASHCARD QUESTION
Front
What is the vertex of a parabola?
Back
The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.
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