Find the Axis of Symmetry for the Quadratic Function: f(x) = x² + 4x

A quadratic function is graphed below.

What is the axis of symmetry for the graph $f(x)=x^2+4x$ ?

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 look at the function coefficients

00:19 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

00:40 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll determine the axis of symmetry using the appropriate formula:

Now, let's work through each step:

Step 1: The quadratic function is $f(x) = x^2 + 4x$ . Here, $a = 1$ , $b = 4$ , and $c = 0$ .

Step 2: Use the axis of symmetry formula $x = -\frac{b}{2a}$ .

Step 3: Substitute the values: $x = -\frac{4}{2 \times 1} = -\frac{4}{2} = -2$

Therefore, the axis of symmetry for the graph is $x = -2$ .