Locate the Vertex of the Parabola: Analyze y = x² - 6

Find the vertex of the parabola

$y=x^2-6$

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the vertex formula to find $h$ and $k$.
• Step 3: Determine the coordinates of the vertex.

Now, let's work through each step:
Step 1: The given quadratic equation is $y = x^2 - 6$ where $a = 1$, $b = 0$, and $c = -6$.
Step 2: We use the vertex formula:

$h = -\frac{b}{2a}$
Substituting the values, $h = -\frac{0}{2 \cdot 1} = 0$.

$k = c - \frac{b^2}{4a}$
Using the given values, $k = -6 - \frac{0^2}{4 \cdot 1} = -6$.

Step 3: Therefore, the vertex of the parabola is at $(h, k) = (0, -6)$.

The solution to the problem is $(0, -6)$.