What does it mean to translate a parabola?

Translating a parabola means shifting its position on the graph without changing its shape. This can be done by adding or subtracting values from $$x$$ or $$y$$ .

How does moving a parabola 5 units to the left affect its equation?

To move a parabola 5 units to the left, replace $$x$$ with $$(x + 5)$$ in the equation. For example, $$y = x^2$$ becomes $$y = (x + 5)^2$$ .

How does moving a parabola 3 units up affect its equation?

To move a parabola 3 units up, add 3 to the entire equation. For example, $$y = x^2$$ becomes $$y = x^2 + 3$$ .

What does it mean to compress a parabola by a factor of 3?

Compressing a parabola by a factor of 3 means multiplying the entire function by $$3$$ . For example, $$y = x^2$$ becomes $$y = 3x^2$$ .

What is the effect of moving a parabola down by 4 units?

Moving a parabola down by 4 units means subtracting 4 from the entire equation. For example, $$y = x^2$$ becomes $$y = x^2 - 4$$ .

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ , where a, b, and c are constants.

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How do you convert from standard form to vertex form?

To convert from standard form to vertex form, complete the square on the quadratic expression.

Quadratic Transformations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What does it mean for a parabola to open upwards?

Back

3.

FLASHCARD QUESTION

Front

What does it mean for a parabola to open downwards?

Back

4.

FLASHCARD QUESTION

Front

How does the value of 'a' affect the width of a parabola?

Back

The value of 'a' affects the width of the parabola: larger absolute values of 'a' make the parabola narrower, while smaller absolute values make it wider.

5.

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.

6.

FLASHCARD QUESTION

Front

How do you find the vertex of a parabola given in standard form?

Back

7.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a parabola?

Back

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