What effect does changing the value of $$a$$ have on the graph of a quadratic function?

Changing the value of $$a$$ affects the width and direction of the parabola. If $$|a| > 1$$ , the parabola is narrower; if $$|a|

How does a negative coefficient affect the graph of a quadratic function?

A negative coefficient for $$a$$ reflects the graph of the quadratic function over the x-axis, causing it to open downwards.

What is the significance of the y-intercept in a quadratic function?

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at $$x = 0$$ , which gives $$f(0) = c$$ .

What is the relationship between the roots of a quadratic function and its graph?

The roots (or zeros) of a quadratic function are the x-values where the graph intersects the x-axis. They can be found using factoring, completing the square, or the quadratic formula.

What is the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What does it mean for a quadratic function to be 'stretched' or 'compressed'?

A quadratic function is 'stretched' when the absolute value of $$a$$ is greater than 1, making the parabola narrower. It is 'compressed' when the absolute value of $$a$$ is less than 1, making the parabola wider.

How do you determine the direction in which a parabola opens?

The direction in which a parabola opens is determined by the sign of the coefficient $$a$$ : if $$a > 0$$ , it opens upwards; if $$a

What is the effect of adding a constant to a quadratic function?

Adding a constant to a quadratic function translates the graph vertically. For example, $$f(x) = x^2 + k$$ shifts the graph up by $$k$$ units if $$k > 0$$ and down if $$k

What is the relationship between the vertex form and standard form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex. The standard form is $$f(x) = ax^2 + bx + c$$ . You can convert between the two forms using completing the square.

5.1 Attributes & 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 the graph of a quadratic function look like?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What does it mean to translate a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is a dilation in the context of quadratic functions?

Back

A dilation changes the size of the graph of a function. A vertical dilation occurs when the function is multiplied by a factor, affecting the steepness of the parabola.

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