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.

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

Video Solution

Solution Steps

00:00 Find the axis of symmetry for the function

00:03 The axis of symmetry is the X value at the vertex point

00:06 The point where if you fold the parabola in half, both halves are identical

00:10 Let's examine the function coefficients

00:18 We'll use the formula to calculate the vertex point

00:23 We'll substitute appropriate values according to the given data and solve for X at the point

00:34 And this is the solution to the question

Step-by-Step Solution

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 $x = -2$ .