Answer:
The equation for the parabola is [tex]y = 2\cdot x^{2}+4\cdot x +3[/tex].
Step-by-step explanation:
Let be [tex]P(x,y) = (2, 19)[/tex], [tex]Q(x,y) = (6,99)[/tex] and [tex]R(x,y) = (-1, 1)[/tex] and quadratic regression is represented by a second-order polynomial of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable
[tex]y[/tex] - Dependent variable
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - 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:
[tex]4\cdot a +2\cdot b + c = 19[/tex] (2)
[tex]36\cdot a + 6\cdot b + c = 99[/tex] (3)
[tex]a -b + c = 1[/tex] (4)
The solution of this system is: [tex]a = 2[/tex], [tex]b = 4[/tex], [tex]c = 3[/tex]. Hence, the equation for the parabola is [tex]y = 2\cdot x^{2}+4\cdot x +3[/tex].
