Why graph of quadratic is always u-shapeddo any coefficient effects the shape of graph of quadratic

graph of quadratic is u-shaped since for every two values of x, there is one y value. that is for both positive and negative signs of x having the same magnitude there is only one y value. the -ve sign is take care by the square part of x. -ve coefficient of x^2 term gets affected the orientation of the curve(either downwards of upwards)

example, 

y = x^2 is an upward curve where as

y=-x^2 is a downward curve