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Hi.
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In this problem, we have a interpreting, interpolating polynomial p of x, which is assumed to be of degree 2, that passes through the points 03 ,15, and 29, and we're asked to find p4.
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So what we're going to do first is find p of x, and then use that to find p of 4.
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So we know that p of x is a degree 2 polynomial.
00:28
So we can write p of x as a x squared plus bx plus c where ab and c are some real numbers some undetermined real numbers so we're going to use the fact that each of the three points we're given um is on this polynomial and that will give us three equations which we'll then use to solve for ab and c so the first point is 03 so the fact that this point is on p of x means that if we plug in x equals 0.
01:09
We should get 3.
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So 3 should be equal to p of 0.
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And if we plug in 0, then this is just c, right? so this is nice.
01:22
We automatically get that c has to be equal to 3.
01:27
And then we do the same thing with the other two points.
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So 1, 5.
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This says that 5 must be equal to p of 1, which is a plus b plus c.
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And we know that c is 3 now.
01:44
So we can say this is a plus b plus 3.
01:47
And so subtracting the three from both sides tells us that a plus b is equal to two.
01:55
So it doesn't tell us a or b specifically, but we have an equation relating them...