
Chapter 3.1 to 3.3 Flashcard SY2023
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What are the zeros of the polynomial y = (x - 5)(x + 2)^2 and their multiplicities?
Back
Zeros: x = 5 (multiplicity 1), x = -2 (multiplicity 2)
2.
FLASHCARD QUESTION
Front
How do you find a polynomial function of degree 3 with given zeros?
Back
To find a polynomial of degree 3 with zeros 3i and -2, use the fact that complex zeros come in conjugate pairs. The polynomial is P(x) = (x - 3i)(x + 3i)(x + 2) = x^3 + 2x^2 + 9x + 18.
3.
FLASHCARD QUESTION
Front
What is the vertex of the parabola given by the equation y = 3(x + 5)^2 - 4?
Back
The vertex is (-5, -4).
4.
FLASHCARD QUESTION
Front
How do you write the standard form equation of a parabola given its vertex and a point it passes through?
Back
Use the vertex form y = a(x - h)^2 + k, where (h, k) is the vertex. Substitute the vertex and the point to find 'a'.
5.
FLASHCARD QUESTION
Front
What is the vertex form equation of a parabola with vertex (-4, 2) and passing through (0, 0)?
Back
The vertex form is f(x) = a(x + 4)^2 + 2. Substitute (0, 0) to find 'a'.
6.
FLASHCARD QUESTION
Front
What is the significance of the multiplicity of a zero in a polynomial?
Back
The multiplicity of a zero indicates how many times that zero is repeated and affects the graph's behavior at that point.
7.
FLASHCARD QUESTION
Front
How do you convert a polynomial from factored form to standard form?
Back
Expand the factors and combine like terms to write the polynomial in standard form.
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