Quadratics Models & transformations
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a quadratic function?
Back
A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What does the graph of a quadratic function look like?
Back
The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.
Tags
CCSS.HSF-IF.C.7A
3.
FLASHCARD QUESTION
Front
What is the vertex of a parabola?
Back
The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the function f(x) = ax^2 + bx + c.
4.
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. It can be found using the formula x = -b/(2a).
5.
FLASHCARD QUESTION
Front
How do transformations affect the graph of a quadratic function?
Back
Transformations such as translations, reflections, and stretches/compressions can change the position and shape of the graph. For example, f(x) = a(x-h)^2 + k translates the graph h units horizontally and k units vertically.
6.
FLASHCARD QUESTION
Front
What is the significance of the 'a' value in a quadratic function?
Back
The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.
7.
FLASHCARD QUESTION
Front
What is the maximum or minimum value of a quadratic function?
Back
The maximum or minimum value occurs at the vertex of the parabola. If the parabola opens upwards, the vertex represents the minimum value; if it opens downwards, it represents the maximum value.
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