Axis of symmetry and Vertex (with Formula) Question Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an \( (x, y) \) point. \[ y=-2 x^{2}-14 \]

To find the vertex of the parabola given by the equation \( y = -2x^2 - 14 \), you can use the vertex formula. For a parabola in the standard form \( y = ax^2 + bx + c \), the x-coordinate of the vertex can be calculated with the formula \( x = -\frac{b}{2a} \). In this case, \( a = -2 \) and \( b = 0 \), so \( x = -\frac{0}{2(-2)} = 0 \). To find the y-coordinate, substitute \( x = 0 \) back into the equation: \( y = -2(0)^2 - 14 = -14 \). Thus, the vertex is at \( (0, -14) \). But did you know that parabolas come into play in many real-life scenarios? From the design of bridges (where arches mimic the shape of a parabola for structural integrity) to the paths of projectiles (like a basketball going through the hoop), understanding parabolic equations helps engineers and scientists alike! When working with parabolas, it’s common to make mistakes with the vertex formula. One common error is forgetting to correctly apply the signs of \( a \) and \( b \) when calculating the vertex's coordinates. Always double-check if \( b \) is zero and make sure to substitute the x-value back into the original equation to find y correctly!