Make this chart:

 x | y
-3 |
-1 |
 0 |
 1 |
 3 |

To find what goes under y besides -3, take the equation:

y = -3x² + 5

and replace x by (-3).  Then you have:

y = -3(-3)² + 5

Square (-3) and get 9. Replace the (-3)² by (9)

y = -3(9) + 5

Multiply the -3 by the 9 and get -27. Replace the -3(9) by -27

y = -27 + 5

Combine -27 and +5 and get -22.  Write -22 besides 3 in
the y-coordinate column:  

 x |  y
-3 | -22  
-1 |
 0 |
 1 |
 3 |
 
I'll skip down to 1 in the x-column: 

To find what goes under y besides 1, take the equation:

y = -3x² + 5

and replace x by (1).  Then you have:

y = -3(1)² + 5

Square (1) and get 1. Replace the (1)² by (1)

y = -3(1) + 5

Multiply the -3 by the 1 and get -3. Replace the -3(1) by -3

y = -3 + 5

Combine -3 and +5 and get 2.  Write 2 besides 1 in
the y-coordinate column:  

 x |  y
-3 |-22  
-1 |  
 0 |
 1 | 2 
 3 |

You can fill in the others just like I filled in those two.

Here are the answers:

 x |  y
-3 |-22  
-1 |  2  
 0 |  5
 1 |  2 
 3 |-22

Edwin