Solving Quadratic Equations

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•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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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 ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What are the x-intercepts of a quadratic equation?
Back
The x-intercepts (or roots) of a quadratic equation are the points where the graph intersects the x-axis, corresponding to the solutions of the equation.
3.
FLASHCARD QUESTION
Front
How can you determine the number of solutions a quadratic equation has?
Back
The number of solutions can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 solutions; D = 0 means 1 solution; D < 0 indicates no real solutions.
4.
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 whether it opens upwards or downwards.
5.
FLASHCARD QUESTION
Front
How do you find the vertex of the parabola given in vertex form y = a(x-h)² + k?
Back
The vertex is the point (h, k).
6.
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 the equation x = -b/(2a).
7.
FLASHCARD QUESTION
Front
What does it mean for a quadratic equation to have no real solutions?
Back
It means that the graph of the quadratic does not intersect the x-axis, which occurs when the discriminant is negative.
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