Determine the maximum of the function x^2-x-6=0.
The vertex is the maximum/minimum point of a parabola.
To find the vertex:
Notice if we eliminate the parentheses, the equation becomes:
x^2-x+1/4-1/4-6=0. Therefore, the value of the equation has not changed.
The vertex of the equation is 1/2, -6.25
However, since the parabola is concave up, the vertex gives only the minimum value. To find the maximum point of the function, we need certain range of x value. If there is no range, then the y-value of function goes to infinity, thus has no maximum point.
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