Question

HELP!!!!

Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(2, 19) (6, 99) (-1, 1)

Answer 1

The equation for the parabola is
`y = 2\cdot x^(2)+4\cdot x +3`.

Explanation:

Let be
`P(x,y) = (2, 19)`,
`Q(x,y) = (6,99)` and
`R(x,y) = (-1, 1)` and quadratic regression is represented by a second-order polynomial of the form:

`y = a\cdot x^(2)+b\cdot x + c` (1)

Where:

`x` - Independent variable

`y` - Dependent variable

`a`,
`b`,
`c` - Coefficients

Algebraically speaking, we need three distinct points on plane to determine the quadratic regression. By using all information, we form the following system of linear equations:

`4\cdot a +2\cdot b + c = 19` (2)

`36\cdot a + 6\cdot b + c = 99` (3)

`a -b + c = 1` (4)

The solution of this system is:
`a = 2`,
`b = 4`,
`c = 3`. Hence, the equation for the parabola is
`y = 2\cdot x^(2)+4\cdot x +3`.