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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 are real numbers.

 Feb 15, 2022
 #1
avatar+36417 
+1

ax^2+bx+c,       when x = 0       then    c = 4

Since it is 'monic'    we know   a = 1

y  =  x^2 +bx   + 4       now when x= 1

10= 1^2 + b + 4      shows b = 5

 

 

y = x^2 + 5x + 4

 Feb 15, 2022
 #2
avatar+122390 
+1

A slight mistake above

 

We know  that c = 4   and a  =1

 

So

 

-10  =  (1)^2  + b(1) + 4 

 

- 10  = 5 + b

 

-10 -5  = b   =  -  15

 

The form is

 

f(x)   =x^2  - 15x  +  4

 

cool cool cool

 Feb 15, 2022
 #3
avatar+36417 
+1

Cphill is correct....    I AGAIN missed the tiny ' - ' sign !

ElectricPavlov  Feb 15, 2022

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