What is the standard form of a quadratic equation?

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Mathematics
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Professional Development
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1.
FLASHCARD QUESTION
Front
Back
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What are the roots of a quadratic equation?
Back
The roots of a quadratic equation are the values of x that satisfy the equation, found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
3.
FLASHCARD QUESTION
Front
How do you factor a quadratic expression like q² + 14q + 48?
Back
To factor q² + 14q + 48, look for two numbers that multiply to 48 and add to 14. The factors are (q + 6)(q + 8).
4.
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.
5.
FLASHCARD QUESTION
Front
What does it mean for a quadratic to have complex roots?
Back
Complex roots occur when the discriminant is negative, resulting in roots that include imaginary numbers.
6.
FLASHCARD QUESTION
Front
How can you determine the vertex of a parabola represented by a quadratic equation?
Back
The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.
7.
FLASHCARD QUESTION
Front
What is the axis of symmetry in a quadratic function?
Back
The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).
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