Question

5. The mapping f: xax² + bx + c defined on the set of real numbers is such that f(0) = -4,f(1)-1 and/(-1)= -5. Find a, b and c. 5 . The mapping f : xax² + bx + c defined on the set of real numbers is such that f ( 0 ) = -4 , f ( 1 ) -1 and / ( - 1 ) = -5 . Find a , b and c .​

Answer 1

It looks like you're saying

`f(x) = ax^2 + bx + c`

and you're asked to find
`a,b,c` given
`f(0)=-4`,
`f(1)=-1`, and
`f(-1)=-5`.

Evaluate
`f` at the three given points:

`x=0 \implies f(0) = \boxed{c = -4}`

`x=1 \implies f(1) = -1 = a + b + c \implies a+b = 3`

`x=-1 \implies f(-1) = -5 = a - b + c \implies a - b = -1`

`(a+b) + (a-b) = 3 + (-1) \implies 2a = 2 \implies \boxed{a=2}`

`a-b = -1 \implies \boxed{b=3}`

and the mapping is
`f(x) = 2x^2 + 3x - 4`.