Question

Let $F\left(x\right)=x^2+4x+1$. Then

• A. $F\left(x\right)>0$ for all $x$
• B. $F\left(x\right)>1$ when $x\ge 0$
• C. $F\left(x\right)\ge 1$ when $x\le -4$
• D. $F\left(x\right)=F(-x)$ for all $x$

Answer 1

Answer: (C)

$F\left(x\right)\ge 1$ when $x\le -4$

$F\left(x\right)=x^2+4x+1$

$=(x+2{)}^2+1-4$

$=(x+2{)}^2-3$

For $x\le -4$

$(x+2{)}^2-3\le -4$

$(x+2{)}^2\le -1$

$\therefore F\left(x\right)\ge 1$

for all $x\le -4$