What does a horizontal shift to the right by 'h' units look like for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = (x - h)^2$$ .

What does a horizontal shift to the left by 'h' units look like for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = (x + h)^2$$ .

What does a vertical shift up by 'k' units look like for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = x^2 + k$$ .

What does a vertical shift down by 'k' units look like for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = x^2 - k$$ .

What is a reflection over the x-axis for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = -x^2$$ .

What is a reflection over the y-axis for the function $$f(x) = x^2$$ ?

The transformed function remains $$g(x) = x^2$$ since it is symmetric about the y-axis.

What does a horizontal stretch by a factor of 'a' look like for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = (x/a)^2$$ .

What does a vertical stretch by a factor of 'a' look like for the function $$f(x) = x^2$$ ?

The transformed function is $$g(x) = a(x^2)$$ .

How do you represent a translation of a quadratic function 4.5 units to the left?

The function is represented as $$g(x) = (x + 4.5)^2$$ .

What is the effect of the transformation $$g(x) = f(x + 2) - 5$$ on the graph of $$f(x) = x^2$$ ?

This represents a horizontal shift left by 2 units and a vertical shift down by 5 units.

What is the general form of a quadratic function?

The general form is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

What is the vertex of the quadratic function $$f(x) = a(x - h)^2 + k$$ ?

The vertex is the point (h, k).

What is the axis of symmetry for the quadratic function $$f(x) = ax^2 + bx + c$$ ?

The axis of symmetry is given by the line $$x = -\frac{b}{2a}$$ .

Transformations of Quadratic Functions Flashcards

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1.

FLASHCARD QUESTION

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What is a transformation of a quadratic function?

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A transformation of a quadratic function involves changing its position, shape, or orientation on the graph, which can include translations, reflections, stretches, and compressions.

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