How does the graph of $$y = (x + 3)^2$$ compare to the parent function $$y = x^2$$ ?

The graph of $$y = (x + 3)^2$$ is a translation of the parent function $$y = x^2$$ . It shifts the graph 3 units to the left.

What effect does changing the coefficient of $$x^2$$ have on the graph of a quadratic function?

Changing the coefficient of $$x^2$$ affects the width and direction of the parabola. A larger coefficient makes the parabola narrower, while a smaller coefficient makes it wider.

What is the standard form of a quadratic function?

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

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; and if $$D

How do you find the y-intercept of a quadratic function?

The y-intercept of a quadratic function can be found by evaluating the function at $$x = 0$$ . For $$y = ax^2 + bx + c$$ , the y-intercept is $$c$$ .

What is the vertex form of a quadratic function?

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

What does it mean for a function to be increasing or decreasing?

A function is increasing on an interval if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

What is a transformation in the context of functions?

A transformation is a change made to a function that alters its graph, such as translations, reflections, stretches, or compressions.

What is the effect of a vertical stretch on the graph of a function?

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller and narrower.

How can you identify the type of function from its graph?

You can identify the type of function by observing the shape of the graph: straight lines indicate linear functions, parabolas indicate quadratic functions, and other shapes indicate different types of functions.

Friday Flashcard 15, Part 2 Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a base for creating more complex functions. Examples include linear functions (y = x), quadratic functions (y = x^2), and cubic functions (y = x^3).

2.

FLASHCARD QUESTION

Front

What is the shape of the graph of a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

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

What is the axis of symmetry in a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and its graph is a straight line, while a quadratic function has a variable rate of change and its graph is a parabola.

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