Grade 11 Math — Functions & Applications · The vertex
The turning point has an address
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The turning point has an address

Every parabola turns exactly once, and the turn has coordinates. The x-coordinate is h=b2ah = -\dfrac{b}{2a} — read aloud: h equals minus b over two a. That vertical line is the axis of symmetry: the graph is its own mirror image across it, which is why h also sits exactly midway between the two roots whenever roots exist.

The height of the turn is k=cb24ak = c - \dfrac{b^2}{4a}k equals c minus b-squared over four a. With a positive, k is the lowest y the function will ever visit; with a negative, the highest — the vertex is where every max-and-min question in this course eventually goes to be answered. Work h first, k second, and mind the signs: −b with b = −8 comes out a cheerful +8.