How does the graph of $$g(x) = 7x^2$$ relate to $$f(x) = x^2$$ ?

The graph of $$g(x) = 7x^2$$ is a dilation of $$f(x) = x^2$$ stretched vertically by a factor of 7.

How does the graph of $$g(x) = \frac{1}{5}x^2$$ relate to $$f(x) = x^2$$ ?

The graph of $$g(x) = \frac{1}{5}x^2$$ is a dilation of $$f(x) = x^2$$ compressed vertically by a factor of 5.

How does the graph of $$g(x) = x^2 + 2$$ relate to $$f(x) = x^2$$ ?

The graph of $$g(x) = x^2 + 2$$ is a translation of $$f(x) = x^2$$ up 2 units.

How does the graph of $$g(x) = (x - 1)^2$$ relate to $$f(x) = x^2$$ ?

The graph of $$g(x) = (x - 1)^2$$ is a translation of $$f(x) = x^2$$ right 1 unit.

How does the graph of $$g(x) = x^2 - 8$$ relate to $$f(x) = x^2$$ ?

The graph of $$g(x) = x^2 - 8$$ is a translation of $$f(x) = x^2$$ down 8 units.

What is the vertex of a quadratic function?

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula $$x = -\frac{b}{2a}$$ .

What does it mean for a quadratic function to open upwards?

A quadratic function opens upwards if the coefficient of $$x^2$$ (a) is positive. This means the vertex is the minimum point.

What does it mean for a quadratic function to open downwards?

A quadratic function opens downwards if the coefficient of $$x^2$$ (a) is negative. This means the vertex is the maximum point.

What is the standard form of a quadratic function?

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

What is the factored form of a quadratic function?

The factored form of a quadratic function is $$f(x) = a(x - r_1)(x - r_2)$$ , where $$r_1$$ and $$r_2$$ are the roots of the function.

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D

Transformations of Quadratic Functions 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 to dilate a function vertically?

Back

Dilation of a function vertically means stretching or compressing the graph of the function along the y-axis. If the factor is greater than 1, it stretches; if it is between 0 and 1, it compresses.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is a translation of a function?

Back

A translation of a function involves shifting the graph of the function horizontally or vertically without changing its shape.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

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Back

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