SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x) = -2x^2+2x+4 The x-Coordinate of the vertex is

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The x-coordinate of the vertex of a parabola in the form is given by .

The y-coordinate is then .

The line of symmetry passes through the vertex, so the equation is .

The maximum or minimum is the value of the function at . Whether it is a maximum or minimum depends on whether the parabola opens up or down. If it is concave up (makes a valley rather than a hill), the point is a minimum, otherwise it is a maximum. You can tell which way the parabola opens by the sign on the lead coefficient. if , it is concave down, if , it is concave up, and, of course, if you don't have a parabola at all.

Let's look at your specific problem:



First thing to note is that , so this is a concave down parabola and the vertex is a maximum.

, so the x-coordinate of the vertex is and the equation of the line of symmetry is .

The value of the function at , denoted for your problem is (not !).

So the y-coordinate of the vertex and the maximum value of f is