Get it into f(x)=a(x-h)²+k form basically complete the square
so steps 1. isolate x terms 2. factor out coefient of x^2 term 3. take 1/2 of linear coefient (x term) and square it and add negative and positive inside of parenthasees 4. factor perfect square 5. expand 6. bow
so f(x)=-3x²-18x-31 group f(x)=(-3x²-18x)-31 undistribute coefient f(x)=-3(x²+6x)-31 take 1/2 of 6 and square it (6/2=3, 3²=9), add positive and negative of it inside f(x)=-3(x²+6x+9-9)-31 factor perfect square f(x)=-3((x+3)²-9)-31 expand/distribue f(x)=-3(x+3)²+27-31 f(x)=-3(x+3)²-4
