Definition: The vertex of a parabola is its turning point, the lowest point if it opens upward or the highest point if it opens downward, lying on the axis of symmetry.
What does the vertex tell you?
It gives the minimum or maximum value of a quadratic function. In a word problem, that might be the greatest height of a thrown ball or the lowest cost of production.
How do you find it?
From standard form ax2 + bx + c, compute x = -b / (2a), then substitute to find y. From vertex form a(x – h)2 + k, read the vertex (h, k) directly.
Example. A ball’s height is h(t) = -5t2 + 30t + 2 meters. The time of greatest height is t = -30 / (2 · -5) = 3 seconds. The height is h(3) = -45 + 90 + 2 = 47 meters. The vertex is (3, 47).
What do students mix up?
In vertex form the x-coordinate is h, but the equation shows x – h, so y = (x + 4)2 + 1 has vertex (-4, 1), not (4, 1). Others report only the x-value. Remember that the vertex is a point, with two coordinates.