Solution: The vertex form of a parabola $ y = ax^2 + bx + c $ has its vertex at $ x = -\frac{b}{2a} $. Here, $ a = -2 $, $ b = 8 $, so $ x = -\frac{8}{2(-2)} = 2 $. Substituting $ x = 2 $ into the equation: $ y = -2(2)^2 + 8(2) - 5 = -8 + 16 - 5 = 3 $. Thus, the vertex is at $ (2, 3) $. \boxed{(2, 3)}

Mon, 04 May 2026 10:56:57 +0000

Mastering Parabolas: Finding the Vertex Using Vertex Form Understanding the shape and position of a parabola is essential in algebra and calculus. One key feature is the vertex — the highest or lowest point depending on the parabola’s direction. For quadratic equations in standard form $ y = ax^2 + bx + c $, calculating the vertex coordinates has a simple, efficient solution known as the vertex formula. ### What Is the Vertex of a Parabola? The vertex of a parabola described by $ y = ax^2 + bx + c $ occurs at
$$
x = -rac{b}{2a}
$$
This formula is derived from completing the square and reveals the axis of symmetry. Once the $ x $-coordinate is found, substituting it back into the equation gives the $ y $-coordinate, pinpointing the exact vertex.