Quadratic Functions: Factored Form Flashcards

Questions and Answers

Which is the graph of f(x) = -(x + 3)(x + 1)?

Graph A

Graph B (correct)

Graph D

Graph C

Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?

Graph A (correct)

Graph D

Graph C

Graph B

The graph of the function f(x) = (x - 4)(x + 1) is shown below. Which statement about the function is true?

Statement D (correct)

Statement C

Statement A

Statement B

Which is the graph of f(x) = (x - 1)(x + 4)?

Graph D Signup and view all the answers

What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)? The axis of symmetry is x =

6 Signup and view all the answers

The function f(x) = −(x + 5)(x + 1) is shown. What is the range of the function?

Range A Signup and view all the answers

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)?

Point D Signup and view all the answers

The function f(x) = (x − 4)(x − 2) is shown. What is the range of the function?

Range D Signup and view all the answers

The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true?

Statement B Signup and view all the answers

What is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)?

Option C Signup and view all the answers

What is the y-intercept of the quadratic function f(x) = (x - 6)(x - 2)?

B Signup and view all the answers

What is the midpoint of the x-intercepts of f(x) = (x - 2)(x - 4)?

D Signup and view all the answers

Which function has only one x-intercept at (−6, 0)?

Graph D Signup and view all the answers

The graph of the function f(x) = (x − 3)(x + 1) is shown. Which describes all of the values for which the graph is positive and decreasing?

Values A Signup and view all the answers

Study Notes

Quadratic Functions: Factored Form

The function f(x) = -(x + 3)(x + 1) has a graph that opens downwards, indicating a maximum point.
The function with x-intercepts at (0, 0) and (4, 0) represents a quadratic that crosses the x-axis twice.
The function f(x) = (x - 4)(x + 1) shows characteristics such as x-intercepts and can be analyzed for key features.
The graph of f(x) = (x - 1)(x + 4) features distinct x-intercepts that can be identified graphically.
The axis of symmetry for f(x) = -(x + 9)(x - 21) is located at x = 6, dividing the graph into two symmetrical halves.
The range of the function f(x) = −(x + 5)(x + 1) is determined by the maximum value since it opens downwards.
For the function f(x) = (x + 6)(x - 3), identifying x-intercepts is crucial for understanding its roots.
The range of f(x) = (x − 4)(x − 2) can be deduced from its vertex, as it opens upwards.
The function f(x) = (x + 2)(x + 6) can be analyzed for true statements regarding its behavior and key attributes.
The y-intercept of f(x) = (x - 8)(x + 3) can be calculated by evaluating the function at x = 0.
The y-intercept for f(x) = (x - 6)(x - 2) is found by substituting 0 into the function.
The midpoint of the x-intercepts for f(x) = (x - 2)(x - 4) provides insights into the vertex's horizontal position.
A quadratic function that has only one x-intercept, such as (−6, 0), is termed a perfect square trinomial.
The function f(x) = (x − 3)(x + 1) is characterized by specific intervals where it is positive and decreasing.

Description

Test your understanding of quadratic functions in factored form with these flashcards. Each card presents a function and challenges you to identify characteristics or graphs related to it. Perfect for students looking to reinforce their algebra skills!