Explanation and Answer:
The graph of y=[tex]x^2[/tex] is a parabola (it looks like a u) that intersects the graph at the origin. These are all shifted variations of that graph, so from that you can figure out their formula by visualizing it.
You can also try substituting numbers into the equations and drawing a graph from that.
Graph A is the y=x^2, shifted to the left, so it becomes [tex]y=x^2+x[/tex]. It's +x because now negative numbers can be gotten from the equation, as compared to before when x^2 gives only positive numbers.
Graph B is [tex]y=x^2+3x[/tex] . Similar to graph A, but now it moves down by more units, because of the 3x.
Graph C is [tex]y=-x^2+2[/tex]. Imaging y=x^2 flipped, it changes from looking like a u to n. That's y=[tex]-x^2[/tex]
Graph D is [tex]y= x^2-x[/tex]. The opposite of Graph A.
