What is Interpolation?

Interpolation is a mathematical method used to estimate unknown values that fall within the range of known data points. Many fields, including mathematics, computer graphics, engineering, data analysis, and scientific computing, often employ interpolation. Using known data points as a point of reference is a mathematical and computational technique for estimating values.

It is often utilized when we need to calculate the value of an equation at points located between the given data points and we have a set of data points. Common interpolation techniques include:

Quadratic Interpolation

A quadratic polynomial is used in the mathematical process of quadratic interpolation to estimate values between data points. When you have a set of three data points and wish to estimate the behaviour of a smooth curve passing through these points, you frequently use this formula. To try to predict intermediate values, the quadratic interpolation method assumes that the fundamental connection between the points follows a parabolic curve (a second-degree polynomial).

Table of Content

  • What is Interpolation?
  • What is Quadratic Interpolation?
  • Quadratic Interpolation Formula
  • Derivation of Quadratic Interpolation Formula
  • Applications of Quadratic Interpolation
  • Limitations of Quadratic Interpolation
  • Solved Problems on Quadratic Interpolation Formula.

Similar Reads

What is Interpolation?

Interpolation is a mathematical method used to estimate unknown values that fall within the range of known data points. Many fields, including mathematics, computer graphics, engineering, data analysis, and scientific computing, often employ interpolation. Using known data points as a point of reference is a mathematical and computational technique for estimating values....

What is Quadratic Interpolation?

Using three known data points and a mathematical technique called quadratic interpolation, one can figure out the value of a function that is unidentified at a given location. It depends on the idea that the underlying connection between the information sets follows a parabolic curve, which is modelled by a quadratic equation....

Quadratic Interpolation Formula

Given three known data points (x₀, y₀), (x₁, y₁), and (x₂, y₂), each of which is composed of an x-value and its corresponding y-value, the quadratic interpolation method is used to obtain an estimated value, y, at a given x-value, x. The quadratic Equation required is given as follows:...

Derivation of Quadratic Interpolation Formula

We assume that we have three data points (x0, y0), (x1, y1), and (x2, y2) and that we are attempting to find a quadratic function that passes across these points in order to develop the quadratic interpolation formula. The form of the quadratic function is:...

Applications of Quadratic Interpolation

Some of its applications are as follows:...

Limitations of Quadratic Interpolation

Quadratic Interpolation has some limitations, which are listed as follows:...

Solved Problems on Quadratic Interpolation Formula.

Problem 1: Suppose we have the following three data points: (x₀, y₀) = (1, 5) (x₁, y₁) = (2, 12) (x₂, y₂) = (3, 23)...

Practice Questions on Quadratic Interpolation

Q1. Given three data points (1,2), (2,3), and (3,5), use quadratic interpolation to estimate the value at x = 2.5....

FAQs Quadratic Interpolation Formula

Define Quadratic Interpolation....

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