9. find the vertrex about

To find the vertex of the parabola given by the equation , we can use the vertex formula. The x-coordinate of the vertex can be found using the formula , where and . Substituting, we get . Next, we plug this back into the equation to find the y-coordinate:

So, the vertex is at .

The vertex of a parabola is its highest or lowest point, depending on the direction it opens. In this case, since the coefficient of is positive, the parabola opens upwards, making the vertex the lowest point. It’s quite like finding a hidden gem in the landscape of quadratic equations – it’s the spot where the function takes a turn!

When working with quadratic functions, it’s common to accidentally mix up the signs or miscalculate the coordinates, especially while substituting values. To avoid these pitfalls, double-check your arithmetic and ensure variables are accurately identified. A checklist approach can be handy: confirm values for and , calculate the vertex correctly, and always verify by plugging back into the original equation. It’s all about taking those extra steps to ensure your vertex quest is a success!