The peaks and valleys of a graph. For a parabola, the vertex is the max (if opening down) or min (if opening up).
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y = a·x·x + b·x + c
Finding the turning point of a parabola
- The vertex x-coordinate is x = −b/(2a).
- Substitute that x back into the function to get the y-value.
- If a > 0 the parabola opens up — the vertex is a minimum.
- If a < 0 it opens down — the vertex is a maximum.
Your turn
Find the minimum of y = x² − 6x + 11.
Recap
- Peaks = maxima, valleys = minima.
- Parabola vertex sits at x = −b/(2a).
- Sign of the leading coefficient tells you max vs min.
Try it
Find min of y = x² − 4x + 7
Vertex at x = −b/2a = 2. y(2) = 4 − 8 + 7 = 3. Min is (2, 3).