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

Answer:

The equation for the parabola is $y = 2\cdot x^{2}+4\cdot x +3$.

Step-by-step 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 $y = 2\cdot x^{2}+4\cdot x +3$.