If the image of quadratic function y = - x ^ 2 + 4x + m-2 is all below the x-axis, then the value range of M is____ | Math enthusiast | Mathematical art

If the image of quadratic function y = - x ^ 2 + 4x + m-2 is all below the x-axis, then the value range of M is____

The graph of quadratic function y = - x ^ 2 + 4x + m-2 is a parabola with opening downward,
Therefore, in order to make the image all under the x-axis, we need to satisfy the discriminant = 4 ^ 2-4 times (- 1) times (m-2)

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