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# \$f(x)\$ is a monic polynomial such that \$f(0)=4\$ and \$f(1)=10\$. If \$f(x)\$ has degree \$2\$, what is \$f(x)\$? Express your answer in the form \$ax

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\$f(x)\$ is a monic polynomial such that \$f(0)=4\$ and \$f(1)=10\$. If \$f(x)\$ has degree \$2\$, what is \$f(x)\$? Express your answer in the form \$ax^2+bx+c\$, where \$a\$, \$b\$, and \$c\$ are real numbers.

michaelcai  Sep 16, 2017

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A monic polynomial is a polynomial where the cofficient of the highest order term is 1. (I didn't know this until now, I had to look it up here.)

f(x) is a monic polynomial with a degree of 2.   So we can say...

f(x)    =    1x2  + bx + c    =    x2 + bx + c

The problem says  f(0) = 4 . So...

f(0)  =  02 + b(0) + c

4   =  0   +   0   + c

4   =  c

Now that we know  c = 4 , we know that  f(x) = x2 + bx + 4 .

The problem says f(1) = 10 . So...

f(1)  =  12 + b(1) + 4

10   =  1  +   b   + 4

10   =  5 + b

5   =  b

Now we know  b = 5  and  c = 4 , so   f(x)  =  x2 + 5x + 4 .

hectictar  Sep 16, 2017
Sort:

#1
+4476
+2

A monic polynomial is a polynomial where the cofficient of the highest order term is 1. (I didn't know this until now, I had to look it up here.)

f(x) is a monic polynomial with a degree of 2.   So we can say...

f(x)    =    1x2  + bx + c    =    x2 + bx + c

The problem says  f(0) = 4 . So...

f(0)  =  02 + b(0) + c

4   =  0   +   0   + c

4   =  c

Now that we know  c = 4 , we know that  f(x) = x2 + bx + 4 .

The problem says f(1) = 10 . So...

f(1)  =  12 + b(1) + 4

10   =  1  +   b   + 4

10   =  5 + b

5   =  b

Now we know  b = 5  and  c = 4 , so   f(x)  =  x2 + 5x + 4 .

hectictar  Sep 16, 2017

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