Using the quadratic formula can be very helpful, especially when you want to find the vertex and the axis of symmetry for a quadratic equation. The formula is:

[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

Let's break this down into simpler parts.

Axis of Symmetry

The axis of symmetry is a straight line that helps show the balance of a parabola. You can find it using this formula:

[ x = \frac{-b}{2a} ]

This formula tells you the $x$-coordinate of the vertex, which is the point where the parabola folds over itself.

Finding the Vertex

Once you know the $x$-coordinate of the vertex, you can find where that vertex is located. To do this, take the $x$ value you found from the axis of symmetry and plug it back into the original quadratic equation:

[ y = ax^2 + bx + c ]

So if you used the axis of symmetry formula to get $x$, you will put it back in like this:

[ y = a\left(\frac{-b}{2a}\right)^2 + b\left(\frac{-b}{2a}\right) + c ]

Now you have both the $x$ and $y$ coordinates. The vertex will be at

[ \left(\frac{-b}{2a}, y\right) ]

Summary

1. Axis of Symmetry: Use ( x = \frac{-b}{2a} ).
2. Vertex: Substitute the $x$ value into the original equation to find $y$.

By following these steps, you can confidently find the vertex and axis of symmetry in quadratic equations. Understanding these concepts will make algebra much easier for you!