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,
,
I'm going to express y as a function of x, like this;
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,
,
your table would look something like this:
+++++++++++++++++++++++++++++++++++++++++++++
|x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|_____|_____|_____|_____|____|____|____|____|
|2x^2 | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
|+4x | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
|+3 | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
|y | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
For another equation, say,
,
your table would look something like this:
+++++++++++++++++++++++++++++++++++++++++++++
|x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|_____|_____|_____|_____|____|____|____|____|
|-x^2 | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
|+x | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
|-10 | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
|y | | | | | | | |
|_____|_____|_____|_____|____|____|____|____|
I hope you understood with those two examples?
Now, for our major question,
, this is how our table might look:
+++++++++++++++++++++++++++++++++++++++++++++
|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 |
|_____|_____|_____|_____|____|____|____|____|
Final table (because we need just x and y values):
+++++++++++++++++++++++++++++++++++++++++++++
|x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|_____|_____|_____|_____|____|____|____|____|
|y | -2 | -4 | -4 | -2 | 2 | 8 | 16 |
|_____|_____|_____|_____|____|____|____|____|
I don't know how to plot graphs properly on this site. When I do, I'll update the graph here.
Hope I helped?