[tex]The\ vertex\ form\ of\ f(x)=ax^2+bx+c\\\\f(x)=a(x-p)^2+q\ where\ p=\dfrac{-b}{2a}\ and\ q=\dfrac{-(b^2-4ac)}{4a}=f(p)\\--------------------------\\\\f(x)=7x^2+42x\\\\a=7;\ b=42;\ c=0\\\\p=\dfrac{-42}{2\cdot7}=-\dfrac{42}{14}=-3\\\\q=f(-3)=7\cdot(-3)^2+42\cdot(-3)=7\cdot9-126=63-126=-63\\\\\boxed{f(x)=7(x+3)^2-63}[/tex]
