# 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

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> 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      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth

 Question 131501: 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: The y-coordinate of the vertex is: The equation of the line of symmetry is x = The maximum/minimum of f(x) is The value, f(1/2) = 17/2 is the minimum or maximum? Answer by solver91311(16868)   (Show Source): You can put this solution on YOUR website!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