Transformations of Quadratic Functions Assignment

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following transforms y = x^2 to the graph of y = (x + 5)^2?

A translation 5 units to the left (correct)
A translation 5 units down
A translation 5 units up
A translation 5 units to the right

Which of the following transforms the graph of y = x^2 to the graph of y = x^2 - 7?

Translation 7 units down (correct)
Translation 7 units up
Translation 7 units to the right
Translation 7 units to the left

The graph of y = -0.2x^2 is _______________ the graph of y = x^2.

wider than and opens in the opposite direction of

The graph of y = 5x^2 is _______________ the graph of y = x^2.

narrower than and opens in the same direction as Signup and view all the answers

Write the equation of the function whose graph is shown.

y = (x - 5)^2 + 3 Signup and view all the answers

To obtain the graph of y = (x - 8)^2, shift the graph of y = x^2 _________.

right, 8 (C) Signup and view all the answers

To obtain the graph of y = x^2 - 6, shift the graph of y = x^2 _________.

down, 6 (D) Signup and view all the answers

Explain the steps you would use to determine the path of the ball given by y = -16x^2 + 32x + 3 in terms of a transformation of the graph of y = x^2.

Complete the square to get the equation in vertex form with a = -16, h = 1, and k = 19. The path is a reflection over the x-axis and narrower. It is also translated right 1 unit and up 19 units. Signup and view all the answers

Which of following is the graph of y = -(x + 1)^2 - 3?

The Third Graph (B) Signup and view all the answers

The vertex of the graph of y = (x - 1)^2 - 5 is

(1, -5) (B) Signup and view all the answers

The vertex of the graph of y = -4(x + 3)^2 + 2 is

(-3, 2) (D) Signup and view all the answers

Complete the statements below that show y = x^2 + 2x - 1 being converted to vertex form. Form a perfect-square trinomial.

y = x^2 + 2x + 1 - 1 - 1 (B) Signup and view all the answers

Enter the values of h and k so that y = x^2 + 6x + 10 is in vertex form.

h = 3, k = 1 Signup and view all the answers

Complete the statements below that show y = 8x^2 + 32x + 17 being converted to vertex form.

y = 8(x^2 + 4x + 4) + 17 - 32 (A), y = 8(x + 2)^2 - 15 (C) Signup and view all the answers

Which of the following statements are true about the graph of f(x) = 6(x + 1)^2 - 9? Check all that apply.

The graph is the same as the graph of f(x) = 6x^2 + 12x - 3. (C), The graph opens upward. (D), The graph is steeper than the graph of f(x) = x^2. (E) Signup and view all the answers

Study Notes

Transformations of Quadratic Functions

Translation Example: The function y = (x + 5)² is derived from y = x² by translating the graph 5 units to the left.
Vertical Translations: The function y = x² - 7 represents a vertical translation of the graph of y = x² downwards by 7 units.
Wider vs. Narrower Graphs: The graph y = -0.2x² is wider than y = x² and opens in the opposite direction, while y = 5x² is narrower than y = x² and opens in the same direction.
Graph Equation Construction: For the function graph, use y = (x + ___)² + ___, with an example being y = (x - 5)² + 3, indicating a horizontal shift to the right by 5 and a vertical shift upwards by 3.
Horizontal and Vertical Shifts: To obtain y = (x - 8)² from y = x², shift right by 8. To convert y = x² to y = x² - 6, shift down by 6.
Projectile Motion Representation: A ball's height, modeled by y = -16x² + 32x + 3, describes a parabolic path. Completing the square reveals a vertex form indicating a reflection across the x-axis, narrower shape, and shifts to the right by 1 unit and up by 19 units.
Identifying Graph Type: The graph of y = -(x + 1)² - 3 is identified as the third graph option.
Finding Vertex Coordinates: The vertex for y = (x - 1)² - 5 is at (1, -5). For y = -4(x + 3)² + 2, the vertex is at (-3, 2).
Vertex Form Conversion Steps: Converting y = x² + 2x - 1 to vertex form involves forming a perfect-square trinomial, factoring it, and simplifying to (x + 1)² - 2.
Finding Vertex Form Parameters: The vertex form of y = x² + 6x + 10 results in y = (x + 3)² + 1 after identifying h = -3 and k = 1.
Converting to Vertex Form with Leading Coefficient: The function y = 8x² + 32x + 17 transforms to vertex form by first factoring out the leading coefficient, leading to y = 8(x + 2)² - 15.
Graph Properties Analysis: For f(x) = 6(x + 1)² - 9, the true statements include that the vertex is not (1, -9), the graph opens upward, the graph is steeper than y = x², and it is equivalent to f(x) = 6x² + 12x - 3.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz focuses on transformations of quadratic functions, specifically how translations and dilations affect the graph of y = x². Test your knowledge of the vertical and horizontal shifts and the effects of changes in the coefficient. Prepare to apply your understanding of these concepts through various scenarios.