Find the maximum or minimum value of quadratic function 𝑦 = 2𝑥2 + 2𝑥 − 3.

To find the maximum or minimum value of a quadratic function, we first need to determine whether the function opens upwards or downwards. This is determined by the coefficient of the x² term. If it's positive, the function opens upwards and has a minimum. If it's negative, the function opens downwards and has a maximum.

In this case, the function y = 2x² + 2x - 3 opens upwards because the coefficient of x² is positive (2). So, this function has a minimum value.

The x-coordinate of the vertex of a parabola given by the equation y = ax² + bx + c is given by -b/2a.

So, for this function, the x-coordinate of the vertex is -b/2a = -2/(2*2) = -0.5.

To find the y-coordinate of the vertex (which is the minimum value of the function), we substitute x = -0.5 into the function:

y = 2(-0.5)² + 2(-0.5) - 3 = 0.5 - 1 - 3 = -3.5.

So, the minimum value of the function y = 2x² + 2x - 3 is -3.5.