Question

attendance over the last nine years with the function
n(t) = 4.32t² - 84.708t + 314.9
which graph would most likely be associated with the given model?

a. graph with year on x - axis and n(t) (students) on y - axis, data points plotted

b. graph with year on x - axis and n(t) (students) on y - axis, data points plotted

c. graph with year on x - axis and n(t) (students) on y - axis, data points plotted

d. graph with year on x - axis and n(t) (students) on y - axis, data points plotted

Explanation:

Step1: Analyze the function type

The given function is \( n(t)=4.32t^{2}-84.708t + 214.9 \), which is a quadratic function (degree 2). The general form of a quadratic function is \( y = ax^{2}+bx + c \), and its graph is a parabola. For \( a = 4.32>0 \), the parabola opens upwards.

Step2: Analyze the graphs

We need to check which graph has a parabolic (upward - opening) trend among the given options. Let's consider the shape of the data points (since these are scatter plots representing the model). A quadratic function with \( a>0 \) will have a U - shaped curve. We look for the graph where the points seem to follow a U - shaped (upward - opening parabola) pattern.

Looking at the options:

• Option A: The points do not show a U - shaped pattern.
• Option B: The points do not show a U - shaped pattern.
• Option C: The points seem to follow a U - shaped (upward - opening) pattern, which is consistent with a quadratic function with \( a = 4.32>0 \).
• Option D: The points do not show a U - shaped pattern.

Answer:

C