From the standard form ax^2 + bx + c, the x-coordinate of the vertex is h = ?

From the standard form ax^2 + bx + c, the x-coordinate of the vertex is h = ?

• A. h = b/(2a)
• B. h = -2a/b
• C. h = -b/(2a)
• D. h = 2a/b

Answer: (C)

The vertex’s x-coordinate comes from the axis of symmetry of the parabola y = ax^2 + bx + c. If you rewrite the quadratic in vertex form y = a(x − h)^2 + k, expanding gives ax^2 − 2ahx + (ah^2 + k). Matching the coefficient of x with bx shows b = −2ah, so h = −b/(2a). Another quick way is to use calculus: take the derivative dy/dx = 2ax + b and set it to zero to find the x-coordinate of the vertex, which gives x = −b/(2a). Therefore, the x-coordinate of the vertex is −b/(2a).

The vertex’s x-coordinate comes from the axis of symmetry of the parabola y = ax^2 + bx + c. If you rewrite the quadratic in vertex form y = a(x − h)^2 + k, expanding gives ax^2 − 2ahx + (ah^2 + k). Matching the coefficient of x with bx shows b = −2ah, so h = −b/(2a). Another quick way is to use calculus: take the derivative dy/dx = 2ax + b and set it to zero to find the x-coordinate of the vertex, which gives x = −b/(2a). Therefore, the x-coordinate of the vertex is −b/(2a).