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What are the coordinates of the vertex of a parabola in standard form $y = ax^2 + bx + c$, and what is the axis of symmetry?

Study flashcard from the deck Digital SAT Math: Algebra, Advanced Math & Geometry.

Answer

The vertex is at $(h, k)$ where $h = -\frac{b}{2a}$ and $k = f\left(-\frac{b}{2a}\right)$. The axis of symmetry is the vertical line $x = -\frac{b}{2a}$.

Explanation

If $a > 0$, the parabola opens upward and $k$ is the minimum value; if $a < 0$, the parabola opens downward and $k$ is the maximum value.

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