Question

Use technology to determine an appropriate model of the data. (-1,0), (1,-4), (2,-3), (4,5), (5,12)

Answer 1

By graphing the points, The best mode of the data will be the quadratic function

There is 5 steps to find the quadratic function that models the data.

First step           ⇒ Plot the data pairs (x, y) in a coordinate plane.
                              which are the blue circles in the attached figure

Second step     ⇒ Draw the parabola you think best fits the data.
                             Which is the red function in the attached figure.

Third step         ⇒ Estimate the coordinates of three points on the
                             parabola, which are (-1, 0), (2, -3), and (5, 12).

Fourth step       ⇒ Substitute the coordinates of the points into the model
                            y = ax² + bx + c
                            to obtain a system of three linear equations.

                            a - b + c = 0           ---------(1)
                            4a + 2 b + c = -3    ---------(2)
                            25a + 5 b + c = 12 ---------(3)   

Fifth step   ⇒ Solve the linear system.
                      By using the calculator
                      a = 1 , b = -2 , c = -3

So, the quadratic model for the data is ⇒ y = x² - 2x - 3