Sure! Finding the vertex of a parabola might seem a bit hard at first, but there's an easy formula to help you out.

The Vertex Formula

For any quadratic equation like ( y = ax^2 + bx + c ), you can find the vertex using these steps:

1. X-Coordinate of the Vertex: $x = -\frac{b}{2a}$

2. Y-Coordinate of the Vertex: Once you have ( x ), just put it back into the original equation to find ( y ): $y = a\left(-\frac{b}{2a}\right)^2 + b\left(-\frac{b}{2a}\right) + c$

Example

Let’s look at the quadratic ( y = 2x^2 + 4x + 1 ).

• Here, ( a = 2 ) and ( b = 4 ).

• First, find the x-coordinate: $x = -\frac{4}{2 \cdot 2} = -\frac{4}{4} = -1$

• Now, put ( x = -1 ) back into the equation to find ( y ): $y = 2(-1)^2 + 4(-1) + 1 = 2 - 4 + 1 = -1$

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

Why It Matters

Knowing the vertex is important because it tells you the highest or lowest point on the parabola. This information helps when you are drawing the graph and understanding how the parabola behaves. So, make sure to use this formula the next time you work with a quadratic equation!