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

Maiclubk 2021-06-13 Answered
Find the quadratic polynomial whose graph passes through the points (0, 0), (-1, 1), and (1, 1).
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Expert Answer

Velsenw
Answered 2021-06-14 Author has 91 answers

Denote the interpolating quadratic polynomial by p(x) = a0+a1x+a2x2
Let's substitute the given points in the equation of the polynomial. The points (0,0), (—1,1) and (1,1) thus have to satisfy
0=a0
1=a0a1+a2
1=a0+a1+a2
We can solve the system by inspection. Substitute ag = 0 into the second and the third equation. We get a system of two equations in two unknowns: a1+a2=1

Sum the equations to get 2a2=2
This implies a2=1. Substituting back into the equations, we get a1=1a2=11=0
Therefore, the interpolating polynomial is p(x)=x2

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Jeffrey Jordon
Answered 2021-10-13 Author has 2495 answers

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