Help quick The engineers designing the All Aboard Railroad between Boca Raton and Jupiter decide to create parallel tracks throu
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Answer:
Procedure:
1) Form a system of 3 linear equations based on the two zeroes and a point.
2) Solve the resulting system by analytical methods.
3) Substitute all coefficients.
Step-by-step explanation:
A quadratic function is a polynomial of the form:
(1)
Where:
- Independent variable.
- Dependent variable.
,
,
- Coefficients.
A value of is a zero of the quadratic function if and only if
. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points:
,
and
Based on such information, we form the following system of linear equations:
(2)
(3)
(4)
There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:
And finally we obtain the equation of the quadratic function given two zeroes and a point.