Find the quadratic polynomial whose graph passes through the points (0, 0), (-1, 1), and (1, 1).

Maiclubk

Maiclubk

Answered question

2021-06-13

Find the quadratic polynomial whose graph passes through the points (0, 0), (-1, 1), and (1, 1).

Answer & Explanation

Velsenw

Velsenw

Skilled2021-06-14Added 91 answers

Interpolating quadratic polynomial is denoted by p(x) = a0+a1x+a2x2
Let's change the supplied points in the polynomial's equation. As a result, the points (0,0), (—1,1), and (1,1) must satisfy.
0=a0
1=a0a1+a2
1=a0+a1+a2
We can examine the system and find a solution. In the second and third equations, enter ag = 0. A set of two equations with two unknowns results: a1+a2=1

Sum the equations to get 2a2=2
This implies a2=1. Reentering the equations yields the following result: a1=1a2=11=0
the interpolating polynomial is hence p(x)=x2

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-13Added 2605 answers

Answer is given below (on video)

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