Question

consider the data set shown in the table.

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
y | 1.5 | 2.2 | 2.7 | 2.6 | 3.5 | 3.8 | 4.0 | 3.4 | 3.2 | 2.9 | 2.8

use an online graphing tool to find the quadratic equation that models the data in this table. for help, see this worked example.
type the correct answer in each box. use numerals instead of words. round your answers to the nearest hundredth.
the quadratic equation that models the data in this table is y = \\(\square\\)\\(x^2\\) + \\(\square\\)x + \\(\square\\).

Explanation:

Step1: Recall quadratic model form

A quadratic model has the form $y = ax^2 + bx + c$, where $a$, $b$, $c$ are coefficients to be found using the given data.

Step2: Input data to regression tool

Enter the paired $(x,y)$ values: $(0,1.5), (1,2.2), (2,2.7), (3,2.6), (4,3.5), (5,3.8), (6,4.0), (7,3.4), (8,3.2), (9,2.9), (10,2.8)$ into a quadratic regression calculator.

Step3: Round coefficients to hundredths

The regression tool outputs $a \approx -0.08$, $b \approx 0.83$, $c \approx 1.52$ after rounding to the nearest hundredth.

Answer:

The quadratic equation that models the data in this table is $y = -0.08x^2 + 0.83x + 1.52$