Finding the vertex of a quadratic equation might seem hard at first, but it's actually pretty easy once you know the steps! A quadratic equation is usually written like this:

$$y = ax^2 + bx + c$$

Let’s break down how to find the vertex step by step:

1. Identify Coefficients

First, you need to find the numbers (a), (b), and (c) in your equation.

For example, if your equation looks like this:

$$y = 2x^2 + 4x + 1$$

Here, (a = 2), (b = 4), and (c = 1).

2. Calculate Axis of Symmetry

The vertex is located on a line called the axis of symmetry. We can find this line using the formula:

$$x = -\frac{b}{2a}$$

Let’s use the numbers from our example:

$$x = -\frac{4}{2(2)} = -\frac{4}{4} = -1$$

3. Find the Vertex Coordinates

Now that you have the x-coordinate of the vertex, we can plug this value back into the original equation to find the y-coordinate:

$$y = 2(-1)^2 + 4(-1) + 1$$

This simplifies to:

$$y = 2(1) - 4 + 1 = -1$$

So the vertex is at the point ((-1, -1)).

Summary

To sum it all up, here are the steps to find the vertex:

• Find the values of (a), (b), and (c).
• Use the formula (x = -\frac{b}{2a}) to find the axis of symmetry.
• Put this x-value back into the equation to get the y-coordinate.

With a little bit of practice, you'll be able to find vertices like a champ!