Describe the steps required to determine the equation of a quadratic function given its zeros and a point.

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.

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step-by-step explanation: