which functions have an axis of symmetry of x = -2? check all that apply.\n□ f(x)=x^{2}+4x + 3\n□…

Explanation:

Step1: Recall axis - of - symmetry formula

For a quadratic function $f(x)=ax^{2}+bx + c$, the axis of symmetry is given by $x =-\frac{b}{2a}$.

Step2: Check $f(x)=x^{2}+4x + 3$

Here $a = 1$, $b = 4$. Then $x=-\frac{4}{2\times1}=- 2$.

Step3: Check $f(x)=x^{2}-4x - 5$

Here $a = 1$, $b=-4$. Then $x=-\frac{-4}{2\times1}=2$.

Step4: Check $f(x)=x^{2}+6x + 2$

Here $a = 1$, $b = 6$. Then $x=-\frac{6}{2\times1}=-3$.

Step5: Check $f(x)=-2x^{2}-8x + 1$

Here $a=-2$, $b=-8$. Then $x=-\frac{-8}{2\times(-2)}=-2$.

Step6: Check $f(x)=-2x^{2}+8x - 2$

Here $a=-2$, $b = 8$. Then $x=-\frac{8}{2\times(-2)} = 2$.

Answer:

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