Question

Find the quadratic function f (x )equals ax squared plus bx plus c for which f (1 )equals negative 2​, f (negative 3 )equals 26​, and f (3 )equals 32.

Answer 1

f(x) =4x² + x - 7

Explanation:

f(x) = ax² + bx + c

f(1) = a + b + c

f(-3) = 9a - 3b + c

f(3) = 9a + 3b + c

a + b + c = -2 -----(1)

c = -2-a-b -----(2)

9a - 3b + c = 26 ------(3)

9a + 3b + c = 32 -------(4)

(2)->(3)

9a-3b-2-a-b = 26

8a-4b = 28

4(2a-b) = 28

2a-b = 7 ----(5)

(2)->(4)

9a+3b-2-a-b = 32

8a+2b = 34

2(4a+b) = 34

4a+b = 17 ----(6)

(5)+(6)

6a = 24

a = 4

sub a=4 into(6)

4(4)+b = 17

b = 1

sub a=4,b=1 into (2)

c = -2-4-1

c = -7