Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
**Which equation(s) represent the graph below?** The graph displayed is a curve with distinct features, including intercepts and turning points. It crosses the x-axis at approximately -4, 2, and 3 and has a y-intercept at around 8. There are noticeable peaks and valleys, with a peak near (-2, 8) and a valley close to (2.5, -5). The graph seems to represent a polynomial function. **Equations:** I: \( y = (x + 2)(x^2 - 4x - 12) \) II: \( y = (x - 3)(x^2 + x - 2) \) III: \( y = (x - 1)(x^2 - 5x - 6) \) **Options:** - ○ I, only - ○ II, only - ○ I and II - ○ II and III
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Transcribed Image Text:**Which equation(s) represent the graph below?** The graph displayed is a curve with distinct features, including intercepts and turning points. It crosses the x-axis at approximately -4, 2, and 3 and has a y-intercept at around 8. There are noticeable peaks and valleys, with a peak near (-2, 8) and a valley close to (2.5, -5). The graph seems to represent a polynomial function. **Equations:** I: \( y = (x + 2)(x^2 - 4x - 12) \) II: \( y = (x - 3)(x^2 + x - 2) \) III: \( y = (x - 1)(x^2 - 5x - 6) \) **Options:** - ○ I, only - ○ II, only - ○ I and II - ○ II and III
Expert Solution
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Step 1

from the graph we can see that x=-2,1,3 are roots of equation.

from (i) we have y=(x+2)(x2-4x-12)=(x+2)(x-6)(x+2)

from(ii) we have y=(x-3)(x2+x-2)=(x-3)(x-1)(x+2)
therefore this equation have also same roots -2,1,3 

also from (iii) we have y=(x-1)(x2-5x-6)=(x-1)(x-6)(x+1)

 

 

bartleby

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