Nonlinear Systems of Equations

Flashcard
•
Mathematics
•
9th - 11th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a nonlinear system of equations?
Back
A system of equations where at least one equation is not linear, meaning it cannot be graphed as a straight line.
2.
FLASHCARD QUESTION
Front
What is the general form of a quadratic equation?
Back
The general form is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
3.
FLASHCARD QUESTION
Front
How do you find the intersection of a linear and a quadratic equation?
Back
Set the equations equal to each other and solve for x, then substitute back to find y.
4.
FLASHCARD QUESTION
Front
What does it mean if a nonlinear system has no solutions?
Back
It means the graphs of the equations do not intersect at any point.
5.
FLASHCARD QUESTION
Front
What is the significance of the vertex in a quadratic function?
Back
The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.
6.
FLASHCARD QUESTION
Front
How can you determine the number of solutions in a linear-quadratic system?
Back
By analyzing the graphs: 0 solutions (no intersection), 1 solution (tangent), or 2 solutions (crossing).
7.
FLASHCARD QUESTION
Front
What is the discriminant in a quadratic equation?
Back
The discriminant is b^2 - 4ac; it determines the nature of the roots (real and distinct, real and equal, or complex).
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