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

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

Denote the interpolating quadratic polynomial by p(x) = $a0+a1x+a2{x}^{2}$
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
$1={a}_{0}-{a}_{1}+{a}_{2}$
$1={a}_{0}+{a}_{1}+{a}_{2}$
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: $-{a}_{1}+{a}_{2}=1$

Sum the equations to get $2{a}_{2}=2$
This implies ${a}_{2}=1$. Substituting back into the equations, we get ${a}_{1}=1-{a}_{2}=1-1=0$
Therefore, the interpolating polynomial is $p\left(x\right)={x}^{2}$

Jeffrey Jordon

Answer is given below (on video)