Find the orthogonal trajectories of family of curves x-y=cx^2

A ball is thrown directly upward from a height of 4ft with an initial velocity of 28 ft/sec. The function s(t)=-16t^2+28t+4 gives the height of the ball,in feet,t seconds after it has been thrown.Determine the time at which the ball reaches its maximum height and find the maximum height.    ^ indicates it to be squared but was not able to find this on my phone so please ensure it's squared thanks

Find the closest and most distant points to the origin on the curve x^2+xy+y^2=1.   Use lagrange multipliers and identify the function and the constraint,

Which is the quadratic parent function?    A y=xy=xy=x    B y=x2y=x^{2}y=x2    C y=xy=\sqrt{x}y=x​    D y=∣x∣y=\left| x\right|y=∣x∣