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How do you graph #y = x^2 - 3#?

Answer 1

See below

I'm assuming that you are familiar with the graph of #f(x)=x^2#, since it is the "standard" parabola:

graph{x^2 [-3, 3, -4.5, 10]}

Now, the function you want to graph is not exactly this one, but they're quite similar: #f(x)=x^2-3# is a transformed version of #f(x)=x^2#.

The tranformation belongs to the following family of transformations:

#f(x) \to f(x)+k#

(in your case, #k=-3#)

This kind of tranformations translate the graph vertically, upwards if #k>0#, downwards otherwise. So, in your case, there will be a shift of three units down. Compare this graph with the first one:

graph{x^2-3 [-3, 3, -4.5, 10]}

you can see how the "shape" is identical, and the only difference is the vertical translation.

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Answer 2

Avery Alexander

To graph the equation ( y = x^2 - 3 ), you can start by creating a table of values for ( x ) and corresponding ( y ) values. Then plot these points on a Cartesian coordinate plane and connect them to form a parabola. Alternatively, you can recognize that the equation represents a parabola that opens upwards with the vertex at (0, -3) and symmetrically increasing on both sides.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.