Avideo game designer decides to include a character in a new game that only moves along a parabolic path. the designer uses the function y = x^2 + 50x + 10 to model this character's path, where y is the height of the character in pixels and the x is the time in seconds that it takes the character to move across one parabolic path. a) find the x-coordinate of the vertex. show all work leading to your answer and write the answer in simplest form. b) find the y-coordinate of the vertex. show all word leading to your answer and write the answer in simplest form. c) what does the vertex represent for this situation? write 1 - 2 sentences to explain your answer.