Answer:
[tex]f(x)=-2(x-2)(x-4)[/tex]
Step-by-step explanation:
If the equation, when graphed, has x-intercepts at (2,0) and (4,0), then it is of the form
[tex]f(x)=a(x-2)(x-4)[/tex]
Open the brackets:
[tex]f(x)=a(x^2-2x-4x+8)\\ \\f(x)=a(x^2-6x+8)\\ \\f(x)=ax^2-6ax+8a[/tex]
This equation has y-intercept at (0,-16), then whan x = 0, f(x) =-16:
[tex]-16=a\cdot 0^2-6a\cdot 0+8a\\ \\8a=-16\\ \\a=-2[/tex]
Therefore,
[tex]f(x)=-2(x-2)(x-4)[/tex]
