Question

which functions have an axis of symmetry of $x = -2$? check all that apply. $f(x)=x^{2}+4x + 3$ $f(x)=x^{2}-4x - 5$ $f(x)=x^{2}+6x + 2$ $f(x)=-2x^{2}-8x + 1$ $f(x)=-2x^{2}+8x - 2$

Explanation:

Step1: Recall axis of symmetry formula

For quadratic $f(x)=ax^2+bx+c$, axis is $x=-\frac{b}{2a}$

Step2: Test $f(x)=x^2+4x+3$

$a=1, b=4$; $x=-\frac{4}{2(1)}=-2$

Step3: Test $f(x)=x^2-4x-5$

$a=1, b=-4$; $x=-\frac{-4}{2(1)}=2$

Step4: Test $f(x)=x^2+6x+2$

$a=1, b=6$; $x=-\frac{6}{2(1)}=-3$

Step5: Test $f(x)=-2x^2-8x+1$

$a=-2, b=-8$; $x=-\frac{-8}{2(-2)}=-2$

Step6: Test $f(x)=-2x^2+8x-2$

$a=-2, b=8$; $x=-\frac{8}{2(-2)}=2$

Answer:

$f(x)=x^2+4x+3$, $f(x)=-2x^2-8x+1$