Since problem says the function is quadratic, it must be a function, except that there is a typo: one of the f(3) must read f(-3). Assuming the last f(3) should read f(-3), then the data now read: f(1) =-7 f(3)=-19 and f(-3)= -49 The general quadratic is f(x)=ax^2+bx+c f(1)=-7 => a+b+c=-7...................(1) f(3)=-19 => 9a+3b+c=-19...........(2) f(-3)=-49 => 9a-3b+c=-49...........(3) (2)-(3) 6b=30 => b=5 (2)-(1) 8a+2b=-12 => 8a+10=-12 => a=(-22/8)=-2.75 substitute a and b in (1) -2.75+5+c=-7 => c=-9.25 => quadratic is -2.75x^2+5x-9.25=0 for f(1) =-7 f(3)=-19 and f(-3)= -49
If the typo is not as assumed above, proceed similarly to get f(x)=-4x^2-5x+2 for f(1) =-7 f(-3)=-19 and f(3)= -49
