Question

Consider the quadratic function f(x) in the form f(x)=1/2 xᵗQx-xᵗb, where Q ∈ Rᵐˣⁿ is a symmetric positive definite matrix, b ∈ Rⁿ, and x ∈ Rⁿ

Answer 1

A quadratic function is a second-order polynomial function, represented by f(x) = (1/2)x^2Qx - x^2b. It can be solved using the quadratic formula or completing the square to find the roots of the function.

Step-by-step explanation:

A quadratic function is a second-order polynomial function. It is of the form f(x) = (1/2)x²Qx - x²b, where Q is a symmetric positive definite matrix, b is a vector, and x is a variable.

The quadratic function represents a curve called a parabola, and it can have one or two roots depending on the discriminant, which is part of the quadratic formula.

To solve the quadratic function, you can use the quadratic formula or complete the square. The roots of the function provide the x-coordinates where the function intersects the x-axis.