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oved Sites (21) Pinterest DeltaMath Chemistry I Hon (22... Desmos | Graphing.... function is defined by the equation y = 2x² + 12x + 24. Which statements are true? Select all that apply. 0 A. The equation written in vertex form is y = 2(x + 3)² + 6. 0 B. The equation written in vertex form is y = 2(x + 3)² + 24. C. The graph of the function has a minimum of y = 6 at x = -3. D D. The domain of the function is all real numbers.

oved Sites (21) Pinterest DeltaMath Chemistry I Hon (22... Desmos | Graphing.... function is defined by the equation y = 2x² + 12x + 24. Which statements are true? Select all that apply. 0 A. The equation written in vertex form is y = 2(x + 3)² + 6. 0 B. The equation written in vertex form is y = 2(x + 3)² + 24. C. The graph of the function has a minimum of y = 6 at x = -3. D D. The domain of the function is all real numbers.

Algebra and Trigonometry (6th Edition)
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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**Title: Understanding Quadratic Functions** A function is defined by the equation \( y = 2x^2 + 12x + 24 \). Which statements are true? Select all that apply. - **A.** The equation written in vertex form is \( y = 2(x + 3)^2 + 6 \). - **B.** The equation written in vertex form is \( y = 2(x + 3)^2 + 24 \). - **C.** The graph of the function has a minimum of \( y = 6 \) at \( x = -3 \). - **D.** The domain of the function is all real numbers. **Explanation**: - **Option A:** Correct transformation of the quadratic equation into vertex form, aligning with standard procedures of completing the square. - **Option B:** Incorrect as it does not match the completed square form. - **Option C:** Describes the vertex of the parabola, which is correct for this equation. - **Option D:** True, as quadratic functions have a domain of all real numbers \((-\infty, \infty)\). *Educational Insight: Understanding these options helps in visualizing and graphing quadratic functions effectively.*
Transcribed Image Text:**Title: Understanding Quadratic Functions** A function is defined by the equation \( y = 2x^2 + 12x + 24 \). Which statements are true? Select all that apply. - **A.** The equation written in vertex form is \( y = 2(x + 3)^2 + 6 \). - **B.** The equation written in vertex form is \( y = 2(x + 3)^2 + 24 \). - **C.** The graph of the function has a minimum of \( y = 6 \) at \( x = -3 \). - **D.** The domain of the function is all real numbers. **Explanation**: - **Option A:** Correct transformation of the quadratic equation into vertex form, aligning with standard procedures of completing the square. - **Option B:** Incorrect as it does not match the completed square form. - **Option C:** Describes the vertex of the parabola, which is correct for this equation. - **Option D:** True, as quadratic functions have a domain of all real numbers \((-\infty, \infty)\). *Educational Insight: Understanding these options helps in visualizing and graphing quadratic functions effectively.*
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