21. hall in terms of time. y -5-3 + postove x-ve HKH 3 X -4y = (x + 3)²-4

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please help me answer question #21 meeting all the conditions a-f. 

Note that this is not graded work. I obtained this question from an old textbook to help me practice solving problem sets. Let me know if you have additional questions. 

The image presents graphs of quadratic functions, each labeled with its equation. Below is a detailed explanation of each graph and the required characteristics:

**Graphs and Functions:**

1. **19. P(x) = (x - 2)²**
   - The graph is a parabola opening upwards with its vertex at (2, 0).
   - **(a)** Vertex: (2, 0)
   - **(b)** Domain: All real numbers; Range: y ≥ 0
   - **(c)** Axis of symmetry: x = 2
   - **(d)** Increasing on (2, ∞)
   - **(e)** Decreasing on (-∞, 2)
   - **(f)** Minimum point at vertex with a minimum value of 0

2. **20. P(x) = (x + 4)²**
   - The graph is a parabola opening upwards with its vertex at (-4, 0).
   - **(a)** Vertex: (-4, 0)
   - **(b)** Domain: All real numbers; Range: y ≥ 0
   - **(c)** Axis of symmetry: x = -4
   - **(d)** Increasing on (-4, ∞)
   - **(e)** Decreasing on (-∞, -4)
   - **(f)** Minimum point at vertex with a minimum value of 0

3. **21. y = (x + 3)² - 4**
   - The graph is a parabola opening upwards with its vertex at (-3, -4).
   - **(a)** Vertex: (-3, -4)
   - **(b)** Domain: All real numbers; Range: y ≥ -4
   - **(c)** Axis of symmetry: x = -3
   - **(d)** Increasing on (-3, ∞)
   - **(e)** Decreasing on (-∞, -3)
   - **(f)** Minimum point at vertex with a minimum value of -4

4. **22. P(x) = -0.5(x + 1)² - 3**
   - The graph is a parabola opening downwards with its vertex at (-1, -3).
   - **(a)** Vertex: (-1, -3)
   - **(b)** Domain: All real numbers;
Transcribed Image Text:The image presents graphs of quadratic functions, each labeled with its equation. Below is a detailed explanation of each graph and the required characteristics: **Graphs and Functions:** 1. **19. P(x) = (x - 2)²** - The graph is a parabola opening upwards with its vertex at (2, 0). - **(a)** Vertex: (2, 0) - **(b)** Domain: All real numbers; Range: y ≥ 0 - **(c)** Axis of symmetry: x = 2 - **(d)** Increasing on (2, ∞) - **(e)** Decreasing on (-∞, 2) - **(f)** Minimum point at vertex with a minimum value of 0 2. **20. P(x) = (x + 4)²** - The graph is a parabola opening upwards with its vertex at (-4, 0). - **(a)** Vertex: (-4, 0) - **(b)** Domain: All real numbers; Range: y ≥ 0 - **(c)** Axis of symmetry: x = -4 - **(d)** Increasing on (-4, ∞) - **(e)** Decreasing on (-∞, -4) - **(f)** Minimum point at vertex with a minimum value of 0 3. **21. y = (x + 3)² - 4** - The graph is a parabola opening upwards with its vertex at (-3, -4). - **(a)** Vertex: (-3, -4) - **(b)** Domain: All real numbers; Range: y ≥ -4 - **(c)** Axis of symmetry: x = -3 - **(d)** Increasing on (-3, ∞) - **(e)** Decreasing on (-∞, -3) - **(f)** Minimum point at vertex with a minimum value of -4 4. **22. P(x) = -0.5(x + 1)² - 3** - The graph is a parabola opening downwards with its vertex at (-1, -3). - **(a)** Vertex: (-1, -3) - **(b)** Domain: All real numbers;
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