Question 752828
An intercept is a point at which the line of a graph crosses the indicated axis.

So, x-intercept is the point where the line cuts or crosses the x-axis while,
y-intercept is the point where the line cuts or crosses the y-axis.

When you want to plot a graph, you have to create a table first for values of both axis ( in physics, sometimes you encounter I/A(current) and V/V (volts), etc.).

For your equation,
{{{-x^2=3x-2}}},
I'm going to express y as a function of x, like this;

{{{y=x^2+3x-2}}}

The only thing I did in the above equation was carrying "-x^2" to the R.H.S and introducing the function, "y".

You'll plot a table of values for the graph.
Now take note, when plotting a table of values, you are to assign a rows for each unit like in the equation below,
{{{y=2x^2+4x+3}}},
your table would look something like this:

<pre>
+++++++++++++++++++++++++++++++++++++++++++++
|x    | -3  | -2  | -1  | 0  | 1  | 2  | 3  |
|_____|_____|_____|_____|____|____|____|____|
|2x^2 |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
|+4x  |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
|+3   |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
|y    |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
</pre>

For another equation, say,
{{{y=-x^2 +x -10}}},
your table would look something like this:

<pre>
+++++++++++++++++++++++++++++++++++++++++++++
|x    | -3  | -2  | -1  | 0  | 1  | 2  | 3  |
|_____|_____|_____|_____|____|____|____|____|
|-x^2 |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
|+x   |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
|-10  |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
|y    |     |     |     |    |    |    |    |
|_____|_____|_____|_____|____|____|____|____|
</pre>

I hope you understood with those two examples?

Now, for our major question,

{{{y=x^2+3x-2}}}, this is how our table might look:

<pre>
+++++++++++++++++++++++++++++++++++++++++++++
|x    | -3  | -2  | -1  | 0  | 1  | 2  | 3  |
|_____|_____|_____|_____|____|____|____|____|
|x^2  |  9  |  4  |  1  | 0  | 1  | 4  | 9  |
|_____|_____|_____|_____|____|____|____|____|
|+3x  | -9  | -6  | -3  | 0  | 3  | 6  | 9  |
|_____|_____|_____|_____|____|____|____|____|
|-2   | -2  | -2  | -2  | -2 | -2 | -2 | -2 |
|_____|_____|_____|_____|____|____|____|____|
|y    |  -2 | -4  | -4  | -2 |  2 |  8 | 16 |
|_____|_____|_____|_____|____|____|____|____|
</pre>

Final table (because we need just x and y values):
<pre>
+++++++++++++++++++++++++++++++++++++++++++++
|x    | -3  | -2  | -1  | 0  | 1  | 2  | 3  |
|_____|_____|_____|_____|____|____|____|____|
|y    | -2  | -4  | -4  | -2 | 2  | 8  | 16 |
|_____|_____|_____|_____|____|____|____|____|
</pre>

I don't know how to plot graphs properly on this site. When I do, I'll update the graph here.

Hope I helped?