Quadratic Function Minimization of it applications

Minimization Quadratic Function in Linear algebra, some applications and examples of it, defined the concept related with Minimization of quadratic function

1. FERGUSSON COLLEGE PUNE Name of students - 1) Satyam Sanjay Wakhare 2) Samruddhi Karande 3) Samruddhi Khobragade Subject - LINEAR ALGEBRA Year - F.Y M.Sc IMCA Guided by – Prof.Vrushali Madam

2. Topic : Applications of Minimization of quadratic function

3. Quadratic Function A quadratic function is a polynomial function of degree two, which means the highest power of the variable (usually x) is two. The general form: f(x) = ax 2  + bx + c where:- a, b, & c are const. This formula is also known as the Sridharacharya formula.

4. Minimization Of Quadratic Function Maximization of Quadratic Function (a<0) Minimization Of Quadratic Function (a>0) Linear Quadratic Function (a=0)

5. DEFINITION All possible values of x ∈ R ; If a>0 ,then the graph of p is a parabola opening upwards ,and so there exists a unique minimum value. That is minimization of Quadratic Function. P(x)= ax 2  + 2bx + c

6. Graphical representation of Quadratic Function MINIMIZATION Maximization LINEAR

7. APPLICATIONS 1. Physics and Engineering : Describe the motion of objects, optimize systems, and minimize energy consumption. 2. Computer Science : Solve algorithmic problems, optimize data structures, and minimize computational complexity. 3. Environmental Science : Optimize resource usage, minimize pollution, and reduce climate change impact. 4.Signal Processing : Filter Design : Minimization of quadratic error functions is used in designing filters that optimally pass desired frequencies while attenuating unwanted ones. Least squares optimization techniques are commonly used in this context.

8. Example 1) y = x 2 - 8x + 14 Put x=4 in above eq n y= 4 2 - 8 * 4 + 14 y= 16 - 32 +14 y= -2 Also put x=2,5 in eq n and then we get values of y = 2, 1 x= |4 | 2 | 5|6| y= |-2 | 2 | 1|2| Plot these values on graph we get parabola

9. References www.google.com Hsc 11 th sci Mathematics Book. Peter J.Olver.Chehrzad Shakiban Book.