Find the maximum or minimum value of quadratic function 𝑦 = 4 − 4𝑥 − 2𝑥2

To find the maximum or minimum value of the quadratic function y = 4 - 4x - 2x^2, we first need to determine whether the function opens upwards or downwards.

The coefficient of x^2 is -2, which is less than 0. This means the parabola opens downwards, so the function has a maximum value.

The x-coordinate of the vertex of a parabola given by y = ax^2 + bx + c is -b/2a.

In this case, a = -2 and b = -4, so the x-coordinate of the vertex is -(-4)/2*(-2) = 1.

Substitute x = 1 into the function to find the maximum value: y = 4 - 41 - 21^2 = 4 - 4 - 2 = -2.

So, the maximum value of the function y = 4 - 4x - 2x^2 is -2.