# Quadratic Lagrange Interpolating Polynomials Examples 1

Recall from the Quadratic Lagrange Interpolating Polynomials page that given three points $(x_0, y_0)$, $(x_1, y_1)$, and $(x_2, y_2)$ where $x_0$, $x_1$, and $x_2$ are distinct numbers, then we can construct a quadratic interpolating polynomial $P_2$ of degree less than or equal to $2$ that interpolates these points where:

(1)The functions $L_0$, $L_1$, and $L_2$ are given by the following formulas:

(2)We will now look at some examples of constructing quadratic Lagrange interpolating polynomials

## Example 1

**Find the quadratic Lagrange interpolating polynomial $P_2$ that interpolates the function $y = \tan x$ at the points $(0, 0)$, $\left ( \frac{\pi}{4}, 1 \right )$, and $(1, \tan(1))$.**

Applying the formula above and we have that:

(5)## Example 2

**Find the quadratic Lagrange interpolating polynomial $P_2$ that interpolates the function $y = e^x$ at the points $(0, 1)$, $(1, e)$, and $(2, e^2)$.**

Applying the formula above and we have that:

(6)