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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.

 Nov 18, 2020
 #1
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A monic polynomial is one where  the lead coefficient on the x^2 term is 1

 

We have the form    f(x)  =   x^2  + bx + c

 

If (0)  = 4   then c  =4

 

And we have that   f(1)  =  10   .....which means that

 

(1)^2  + b(1) + 4 = 10

 

5 + b =  10

 

b  = 5

 

 

So

 

f(x)  = 1x^2 + 5x  + 4

 

 

cool cool cool

 Nov 18, 2020

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