LR Quiz Determinining shape of Loss function

Quiz: Suppose instead of using negative of log-likelihood as the loss, you decide to use least square loss which is defined as Σ(y - y_pred)^2, assuming binary classification, which of the following statements is true about the loss

How can we prove the shape of the graph? Whether it would be convex or concave or kind of mix of them, so multiple minima and maxima will be present