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.

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

4x and 6y

im not sure though