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Find the vertex, Line of symmetry (LOS), Maximum (or minimum).
1) The x-coordinate of the vertex is given by:
The a and b come from the general form of the quadratic equation:
, so a = 1 and b = -12.
The y-coordinate is found by substituting this value of into the given quadratic equation and solving for y, thus: (Change f(x) to y).
Substitute x = 6.
The vertex is at (6, -41)
The equation of the line of symmetry is simply:
This equation, when graphed, will show a parabola that opens upwards and therefore its vertex will be at its minimum point.
You can tell which way the parabola opens by inspecting the coefficient of the
If a is positive, the parabola opens upwards.
If a is negative, the parabola opens downwards. Here's the graph.