Determine the Axis of Symmetry of the Quadratic Function f(x) = x^2 + 4x + 1

Given the expression of the quadratic function

The symmetrical axis of the expression must be found.

$f(x)=x^2+4x+1$

To solve this problem, we'll apply the formula for finding the axis of symmetry for a quadratic function:

• Step 1: Identify the coefficients.
  For the quadratic function $f(x) = x^2 + 4x + 1$, we have $a = 1$ and $b = 4$.
• Step 2: Use the formula for the axis of symmetry.
  The axis of symmetry for a quadratic function $ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$.
• Step 3: Substitute the values of $a$ and $b$ into the formula.
  Substitute $b = 4$ and $a = 1$ to get: $x = -\frac{4}{2 \times 1}$.
• Step 4: Simplify to find the value of $x$.
  This simplifies to $x = -\frac{4}{2} = -2$.

Therefore, the axis of symmetry for the given quadratic function is $x = -2$.