suppose f is a quardratic function for which f(0)=3, f(1)=7 and f(-3)=9[f(1)] find f?

Answer 1

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

f(0) = c = 3

f(1) = a + b + c = 7
--> a + b = 4

f(-3) = 9a -3b +c = 9*f(1) = 63
9a -3b + c = 63
9a -3b = 60
9a - 3(4-a) = 60
9a -12 +3a = 60
12a = 72
a = 6
b = -2

f(x) = 6x^2 -2x +3

Answer 2

f(0) = 3

this gives us

f(x) = ax^2 + bx + 3

f(1) = 7
7 = a(1)^2 + b(1) + 3
a + b = 4

f(-3) = 9f(1)

well we already know that f(1) = 7, so f(-3) = 9(7)
f(-3) = 63

so now we have

63 = a(-3)^2 + b(-3) + 3
9a - 3b = 60
3a - b = 20
-b = -3a + 20
b = 3a - 20

so now we have

a + b = 4
a + (3a - 20) = 4
a + 3a - 20 = 4
4a - 20 = 4
a - 5 = 1
a = 6

b = 3a - 20
b = 3(6) - 20
b = 18 - 20
b = -2

ANS : f(x) = 6x^2 - 2x + 3