Festival attendance: a quadratic model

Name: ______________________ Date: ____________ Festival attendance: a quadratic model (6 points)

Table

A town counts the people who attend its street festival each day. The table gives the attendance

A

, in hundreds of people, on selected days

d

of the festival, where

d = 1

is the first day. The attendance is modeled by the quadratic function

A(d) = ad^2 + bd + c

, whose graph passes through the three data points.

Attendance A, in hundreds of people, on day d of the festival
$d$ (day)	1	4	7
$A$ (hundreds of people)	4.2	9.6	8.4

(A(i)) Use the given data to write three equations that can be used to find the values of the constants $a$ , $b$ and $c$ in the expression for $A(d)$ . [1 point]
(A(ii)) Find the values of $a$ , $b$ and $c$ as decimal approximations. [1 point]
(B(i)) Find the average rate of change of $A$ over the interval $1 \le d \le 7$ . Express your answer using correct units. [1 point]
(B(ii)) The average rate of change from part B(i) is the slope of a secant line. Use this secant line to estimate the attendance on day $d = 5$ . Show the work that leads to your answer. [1 point]
(C) The town wants to use $A$ to plan for later days. Determine the largest day $d$ for which the model gives a reasonable attendance, and explain, using the model, why the model should not be used for days after that. [2 points]

The question