how was the y=x^2 transformed?The blue line is y=x^2the red one y=-28/289(x-21)^2+28 ### Understanding Graph TranslationsIn this lesson, we will explore the concept of translating graphs of functions.#### Example:1. **Equations Displayed:** - \( y = x^2 \) (Blue graph) - \( y = -\frac{28}{289}(x - 21)^2 - 28 \) (Red graph)2. **Graph Descriptions:** - **Blue Graph:** This is a standard parabolic graph representing the quadratic function \( y = x^2 \). The graph opens upwards and is centered at the origin (0,0). - **Red Graph:** This is another parabolic graph represented by the equation \( y = -\frac{28}{289}(x - 21)^2 - 28 \). This graph opens downwards due to the negative leading coefficient and is shifted compared to the blue graph.3. **Key Points:** - The blue graph intersects the y-axis at the origin \((0, 0)\). - The red graph has a vertex at the point \((21, -28)\) due to the translation and transformation of the standard parabola.4. **Translations:** - From \( y = x^2 \) to \( y = -\frac{28}{289}(x - 21)^2 - 28 \): - **Horizontal shift:** The red graph is moved 21 units to the right, evident from the term \( (x - 21) \). - **Vertical shift:** It is moved 28 units down, represented by the -28 outside the squared term. - **Vertical stretch and reflection:** The term \(-\frac{28}{289}\) shows that the graph is reflected over the x-axis (negative coefficient) and also stretched vertically by \(\frac{28}{289}\).5. **Key Points Identified:** - For the red graph, the points identified are near \( (0, 9) \) and \( (0, 35) \), indicating important intersections or features, which are points where you might need to analyze how the function behaves.#### Instruction:**Find the translations:**Analyze how each term in the equation affects the graph from the original function \( y = x^2 \). Understand how horizontal shifts, vertical shifts, and stretching/compressing change the graph's shape and position.### ConclusionUnderstanding the impact

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Answered: how was the y=x^2 transformed? The blue…

how was the y=x^2 transformed? The blue line is y=x^2 the red one y=-28/289(x-21)^2+28

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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