Question

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

Explanation:

The formula for the axis of symmetry of a quadratic function \( f(x) = ax^2 + bx + c \) is \( x = -\frac{b}{2a} \). We will apply this formula to each function.

Step 1: Analyze \( f(x) = x^2 + 4x + 3 \)

Here, \( a = 1 \), \( b = 4 \).
Using the axis of symmetry formula: \( x = -\frac{4}{2(1)} = -2 \). So this function has an axis of symmetry of \( x = -2 \).

Step 2: Analyze \( f(x) = x^2 - 4x - 5 \)

Here, \( a = 1 \), \( b = -4 \).
Using the formula: \( x = -\frac{-4}{2(1)} = 2 \). So this function does not have an axis of symmetry of \( x = -2 \).

Step 3: Analyze \( f(x) = x^2 + 6x + 2 \)

Here, \( a = 1 \), \( b = 6 \).
Using the formula: \( x = -\frac{6}{2(1)} = -3 \). So this function does not have an axis of symmetry of \( x = -2 \).

Step 4: Analyze \( f(x) = -2x^2 - 8x + 1 \)

Here, \( a = -2 \), \( b = -8 \).
Using the formula: \( x = -\frac{-8}{2(-2)} = -\frac{8}{4} = -2 \). So this function has an axis of symmetry of \( x = -2 \).

Step 5: Analyze \( f(x) = -2x^2 + 8x - 2 \)

Here, \( a = -2 \), \( b = 8 \).
Using the formula: \( x = -\frac{8}{2(-2)} = -\frac{8}{-4} = 2 \). So this function does not have an axis of symmetry of \( x = -2 \).

Answer:

The functions with an axis of symmetry of \( x = -2 \) are:

• \( f(x) = x^2 + 4x + 3 \)
• \( f(x) = -2x^2 - 8x + 1 \)