One Parabola For Each Value of c?

The equation y = x^2 + c defines a family of parabolas, one parabola for each value of c. On one set of coordinates axes, graph the members of the family for c = 0, c = 3 and c = -2.

One Parabola For Each Value of c?
Let us consider the parabola where c = 0


y = x^2


Let x = -2, -1, 0, 1 and 2.


We find y = 4, 1, 0 ,1 and 4 in that order.


Graph those points and you will get a basic parabola, a U shaped curve. As x continues to move to the right and left the cure should get steeper and steeper. (It does not curve back on itself as does a circle. You can also try substituting -3 and 3 for x.)


Having suggested that approach for y = x^2. You should use the same x values for:


y = x^2 -2 and y =x^2 +3. If you really want to understand this concept I would suggest you go a step further and try y = x^2 +1
Reply:Giving a representation of a graph, let alone a curved graph, on here as an answer is nigh impossible. However, you may see how they look at this website: http://www.calc5.com/#graph(x*x%2C%20x*x...