How do you graph the function y=x^2-4 and how is the graph a translation of f(x)=x^2

excellent graphing help can be found at

http://rechneronline.de/function-graphs/

where you can plot up to three functions on the same axes.

Note that x^2-4 = (x-2)^2, so it is the graph of x^2, shifted 2 units to the right.

Zowie! Did I say that?

x^2 - 4 is the graph of x^2 shifted down 4 units.

To graph the function y = x^2 - 4 and understand how it is a translation of f(x) = x^2, here are the steps:

1. Start by plotting the graph of the parent function f(x) = x^2. This is a simple parabola centered at the origin, passing through the point (0,0) and symmetric about the y-axis.

2. To create the graph of y = x^2 - 4 (a translation of f(x) = x^2), you need to shift the entire graph downward by 4 units. This means that for each point (x, y) on the original graph of f(x) = x^2, the corresponding point on y = x^2 - 4 will be (x, y - 4).

3. To find a few specific points on the graph of y = x^2 - 4, substitute some x-values into the equation and evaluate y. For example, if you substitute x = 0, you get y = 0^2 - 4 = -4. So, on the new graph, you can plot the point (0, -4).

4. Similarly, substitute x = 1, 2, -1, -2, etc., and calculate the corresponding y-values. Plot these points on the graph, and you will start to see the shape of the parabola shifted 4 units downward.

5. Connect the plotted points with a smooth curve to complete the graph of y = x^2 - 4. The resulting parabola will be identical in shape to the original parabola, but it will be lower on the y-axis by 4 units.

By applying these steps, you will be able to graph y = x^2 - 4 and observe how it is a translation of the original function f(x) = x^2.