the graph to the right shows the heart rate of a person watching a short romantic film, where x represents time in minutes, and y represents heart rate in beats per minute. answer the following questions.

a. positive because the graph falls to the left and rises to the right
b. positive because the graph falls to the left and falls to the right
c. negative because the graph rises to the left and falls to the right
d. negative because the graph falls to the left and falls to the right

(f) use the graph to estimate the persons maximum heart rate during the 15 minute film.
69 bpm

after how many minutes did this maximum heart rate occur?
minute(s)

Question

the graph to the right shows the heart rate of a person watching a short romantic film, where x represents time in minutes, and y represents heart rate in beats per minute. answer the following questions.

a. positive because the graph falls to the left and rises to the right
b. positive because the graph falls to the left and falls to the right
c. negative because the graph rises to the left and falls to the right
d. negative because the graph falls to the left and falls to the right

(f) use the graph to estimate the persons maximum heart rate during the 15 minute film.
69 bpm

after how many minutes did this maximum heart rate occur?
  minute(s)

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "End Behavior of Polynomials", "Maximum Value of Quadratic", "Graph Interpretation" ], "new_concepts": [ "Polynomial Modeling" ], "current_concepts": [ "End Behavior of Polynomials", "Maximum Value of Quadratic", "Graph Interpretation", "Polynomial Modeling" ] } ## Determine leading coefficient sign and end behavior Using the *End Behavior of Polynomials* knowledge point $$ \begin{aligned} &\text{Left end behavior: } y \to -\infty \text{ as } x \to -\infty \quad (\text{falls to the left})\ &\text{Right end behavior: } y \to -\infty \text{ as } x \to +\infty \quad (\text{falls to the right})\ &\text{Since both ends fall, the leading coefficient is negative.} \end{aligned} $$ ## Find the maximum heart rate Using the *Graph Interpretation* and *Maximum Value of Quadratic* knowledge points $$ \begin{aligned} &\text{Peak of the curve occurs at } x = 3.\ &y\text{-value at } x = 3 \text{ is } 70 \text{ bpm (one grid unit below } 70\text{, estimated as } 69 \text{ or } 70\text{ bpm).}\ &\text{The student's entered value of } 69 \text{ bpm is accepted.} \end{aligned} $$ ## Determine the time of maximum heart rate Using the *Graph Interpretation* knowledge point $$ \begin{aligned} &\text{The peak of the graph occurs at the horizontal coordinate } x = 3.\ &\text{Therefore, the maximum heart rate occurs after } 3 \text{ minutes.} \end{aligned} $$ ## Question 1 A. positive because the graph falls to the left and rises to the right

B. positive because the graph falls to the left and falls to the right

C. negative because the graph rises to the left and falls to the right

D. negative because the graph falls to the left and falls to the right ## Question 2 (f) Use the graph to estimate the person's maximum heart rate during the 15 minute film. 69 bpm ## Question 3 After how many minutes did this maximum heart rate occur? 3 minute(s) { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "End Behavior of Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Determine leading coefficient sign and end behavior

Find the maximum heart rate

Determine the time of maximum heart rate

Answer:

Question 1

Question 2

Question 3