Find the vertex of the function (f(x) = -2x^2 + 4x + 5).

Question

Accepted Answer

Step:1 ：The vertex form of a quadratic function is (f(x) = a(x - h)^2 + k), where the vertex of the parabola is at point (h, k).Step:2 ：The x-coordinate of the vertex can be found using the formula (h = -frac{b}{2a}). For the given function, a = -2 and b = 4, so (h = -frac{4}{2*(-2)} = 1).Step:3 ：Substitute x = 1 into the function to find y-coordinate of the vertex: (f(1) = -2*1^2 + 4*1 + 5 = 7).Step:4 ：Therefore, the vertex of the function is at point (1, 7).

Answer

Step: 1 ：The vertex form of a quadratic function is (f(x) = a(x - h)^2 + k), where the vertex of the parabola is at point (h, k).Step: 2 ：The x-coordinate of the vertex can be found using the formula (h = -frac{b}{2a}). For the given function, a = -2 and b = 4, so (h = -frac{4}{2*(-2)} = 1).Step: 3 ：Substitute x = 1 into the function to find y-coordinate of the vertex: (f(1) = -2*1^2 + 4*1 + 5 = 7).Step: 4 ：Therefore, the vertex of the function is at point (1, 7).

Find the vertex of the function \(f(x) = -2x^2 + 4x + 5\).

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