Characteristics of Quadratic Equations

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•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a quadratic equation?
Back
A quadratic equation is a polynomial equation of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What is the standard form of a quadratic equation?
Back
The standard form of a quadratic equation is f(x) = ax² + bx + c.
3.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic equation?
Back
The vertex form of a quadratic equation is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
4.
FLASHCARD QUESTION
Front
How do you find the y-intercept of a quadratic function?
Back
To find the y-intercept, set x = 0 in the equation and solve for f(0).
5.
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 images, given by the formula x = -b/(2a).
6.
FLASHCARD QUESTION
Front
What are the zeros of a quadratic function?
Back
The zeros (or roots) are the values of x for which f(x) = 0, representing the points where the graph intersects the x-axis.
7.
FLASHCARD QUESTION
Front
How can you determine the number of real roots of a quadratic equation?
Back
The number of real roots can be determined using the discriminant, D = b² - 4ac. If D > 0, there are 2 real roots; D = 0, 1 real root; D < 0, no real roots.
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