Podcast
Questions and Answers
What is the vertex of the parabola defined by the function $f(x) = a(x-a)^2$?
What is the vertex of the parabola defined by the function $f(x) = a(x-a)^2$?
- $(0, 0)$
- $(a, 0)$ (correct)
- $(a, a)$
- $(0, a)$
If $a > 0$ in the function $f(x) = a(x-a)^2$, which direction does the parabola open?
If $a > 0$ in the function $f(x) = a(x-a)^2$, which direction does the parabola open?
- Upwards (correct)
- To the right
- To the left
- Downwards
If $a < 0$ in the function $f(x) = a(x-a)^2$, what happens to the function's value as x increases to the right of the vertex?
If $a < 0$ in the function $f(x) = a(x-a)^2$, what happens to the function's value as x increases to the right of the vertex?
- The function remains constant
- The function decreases (falls) (correct)
- The function increases (rises)
- The function oscillates
Which transformation is applied to the parabola $f(x) = ax^2$ to obtain the graph of $f(x) = a(x-a)^2$?
Which transformation is applied to the parabola $f(x) = ax^2$ to obtain the graph of $f(x) = a(x-a)^2$?
For the function $y = -2(x - 1)^2$, what translation occurs compared to $y = -2x^2$?
For the function $y = -2(x - 1)^2$, what translation occurs compared to $y = -2x^2$?
What type of transformation is shifting a graph horizontally or vertically?
What type of transformation is shifting a graph horizontally or vertically?
What is the name of the vertical line that divides a parabola into two symmetrical halves?
What is the name of the vertical line that divides a parabola into two symmetrical halves?
How does the graph of $y = x^2$ change to become the graph of $y = (x-3)^2$?
How does the graph of $y = x^2$ change to become the graph of $y = (x-3)^2$?
What is the turning point of a parabola called?
What is the turning point of a parabola called?
Which equation represents a parabola?
Which equation represents a parabola?
What kind of transformation is represented by the equation $f(x) = (x + 2)$ relative to $f(x) = x$?
What kind of transformation is represented by the equation $f(x) = (x + 2)$ relative to $f(x) = x$?
Which of the following functions represents a shift of the graph $y = x^2$?
Which of the following functions represents a shift of the graph $y = x^2$?
What effect does the 'a' value have on the graph of the function $y = a(x-h)^2$?
What effect does the 'a' value have on the graph of the function $y = a(x-h)^2$?
Flashcards
Vertex of parabola
Vertex of parabola
The point where the parabola changes direction, located at T(a, 0).
Translation of parabola
Translation of parabola
Shifting the graph of the parabola horizontally based on the value of 'a'.
Direction of opening
Direction of opening
A parabola opens upwards if a > 0 and downwards if a < 0.
Graph: f(x) = a(x-a)^2
Graph: f(x) = a(x-a)^2
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Increasing/Decreasing function
Increasing/Decreasing function
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Graph of a Function
Graph of a Function
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Parabola
Parabola
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Axis of Symmetry
Axis of Symmetry
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Translations of Functions
Translations of Functions
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Transformations of Parabolas
Transformations of Parabolas
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Horizontal Translation
Horizontal Translation
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Quadratic Function
Quadratic Function
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