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The annual enrollment of a university for the last nine years is recorded in the table below:

| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|------|----|----|----|----|----|----|----|----|----|
| Students (thousands) | 9.5 | 8 | 8.5 | 7.5 | 6.5 | 6.5 | 8.5 | 8.5 | 9 |

What quadratic function best models this set of data?

[tex]\( y = \square x^2 + \square x + \square \)[/tex]

Sagot :

GinnyAnswer
To find the quadratic function that best models this data set, we follow these steps:

1. Identify the form of the quadratic equation: [tex]\( y = ax^2 + bx + c \)[/tex].

2. Using statistical methods to fit a quadratic model to the given data points representing the years (x) and the number of students (y), we find the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].

3. The result from the fitting process provides the coefficients:
- [tex]\( a = 0.140 \)[/tex]
- [tex]\( b = -1.427 \)[/tex]
- [tex]\( c = 10.75 \)[/tex]

Therefore, the quadratic function that best models the set of data is:
[tex]\[ y = 0.140x^2 - 1.427x + 10.75 \][/tex]

Now, fill in the blanks in the quadratic function:
[tex]\[ y = \boxed{0.140}x^2 + \boxed{-1.427}x + \boxed{10.75} \][/tex]
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