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Advanced Math / Nonlinear functions Difficulty: Easy

$y = - \frac{1}{4} x^{2} + 2 x + 29$

The given equation models a company’s scheduled deliveries over $8$ months, where $y$ is the estimated number of scheduled deliveries $x$ months after the end of May $2012$ , where $0 \leq x \leq 8$ . Which statement is the best interpretation of the y-intercept of the graph of this equation in the xy-plane?

At the end of May $2012$ , the estimated number of scheduled deliveries was $0$ .

At the end of May $2012$ , the estimated number of scheduled deliveries was $29$ .

At the end of June $2012$ , the estimated number of scheduled deliveries was $0$ .

At the end of June $2012$ , the estimated number of scheduled deliveries was $29$ .

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Explanation

Choice B is correct. The y-intercept of a graph in the xy-plane is the point where $x equals 0$ . For the given equation, the y-intercept of the graph in the xy-plane can be found by substituting $0$ for $x$ in the equation, which yields $y = - \frac{1}{4} {(0)}^{2} + 2 (0) + 29$ , or $y equals 29$ . Therefore, the y-intercept of the graph is $left parenthesis 0 comma 29 right parenthesis$ . It’s given that $y$ is the estimated number of scheduled deliveries $x$ months after the end of May $2012$ . Therefore, $x equals 0$ represents $0$ months after the end of May $2012$ , or the end of May $2012$ . Thus, the best interpretation of the y-intercept of the graph of this equation in the xy-plane is that at the end of May $2012$ , the estimated number of scheduled deliveries was $29$ .

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.