Answer:
Please see below.
Step-by-step explanation:
f(x) is a quadratic polynomial. Its two roots are given: x=2, and x=4.
This means that
[tex]f(x) = 0 = d\cdot(x-2)\cdot(x-4) = d\cdot(x^2-6x+8)[/tex]
with d some unknown constant that stretches the parabola along the y axis. Since we are also given f(1), d can be determined:
[tex]f(x) = d\cdot(x^2-6x+8)\\f(1)=3d=6\implies d=2\\\mbox{so}\\f(x) = 2\cdot(x^2-6x+8)=2x^2-12x+16\\\mbox{so}\\a=2, b=-12, c=16[/tex]
