Transformations Of Quadratics

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•
Mathematics
•
9th - 10th Grade
•
Hard
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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 in the form f(x) = ax² + 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'.
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 (-b/2a, f(-b/2a)).
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, given by the equation x = -b/2a.
5.
FLASHCARD QUESTION
Front
What does it mean to shift a graph vertically?
Back
Shifting a graph vertically means moving it up or down without changing its shape. For example, f(x) = x² + k shifts the graph up if k > 0 and down if k < 0.
6.
FLASHCARD QUESTION
Front
What does it mean to shift a graph horizontally?
Back
Shifting a graph horizontally means moving it left or right. For example, f(x) = (x - h)² shifts the graph right if h > 0 and left if h < 0.
7.
FLASHCARD QUESTION
Front
What is a reflection in the x-axis?
Back
A reflection in the x-axis occurs when the graph of a function f(x) is transformed to -f(x), flipping it over the x-axis.
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