Finding the Axis of Symmetry in the Quadratic Equation f(x) = 3x^2 + 2

A quadratic equation is graphed below.

What is the axis of symmetry for the graph $f(x)=3x^2+2$ ?

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's coefficients

00:17 We'll use the formula to calculate the vertex point

00:21 We'll substitute appropriate values according to the given data and solve for X at the point

00:30 And this is the solution to the question

Step-by-Step Solution

To determine the axis of symmetry for the function $f(x) = 3x^2 + 2$ , we follow these steps:

Identify the coefficients from the function. Here, $a = 3$ and $b = 0$ . The constant term $c = 2$ does not affect the axis of symmetry.
Use the axis of symmetry formula for a quadratic function: $x = -\frac{b}{2a}$ .
Substitute the values for $b$ and $a$ into the formula: $x = -\frac{0}{2 \times 3} = 0$ .

This calculation shows that the axis of symmetry for the graph of the quadratic function is $x = 0$ .

Thus, the solution to the problem is that the axis of symmetry is $x = 0$ .