Question

How do you evaluate `3x^2-2x+1` given x=-2, y=-3, z=5?

Answer 1

Are you sure you wrote the question correctly? Anyway, see below

Explanation:

If we want to evaluate an expression depending on some variables, we need to fix a particular value for those variables. This is what happens when you write "given `x=-2, y=-3, z=5`".

Nevertheless, your expression `3x^2-2x+1` only depends on `x`, so fixing a value for `y` and `z` seems quite pointless.

I hope this example can clarify: suppose you are in front of a robot that reads your age and determines whether you can play a video game or not. Suppose the video game is only for people aged `14` or more.

So, if you write "`10`" on the robot keypad, it will answer "you can't play!". Same if you type `13`, but if you type `16` you're good to go.

Now, what happens if you type something like "I'm 19 and my name is Paul?" Well, you're surely good for the game, but what was the point in saying your name as well?

The same goes here: since your expression (assuming you wrote it correctly) only depends on `x`, the values of `y` and `z` are completely out of context.

Anyway, we can still evaluate the expression given `x=-2` which means that we must substitute every occurrence of `x` with `-2`, so the expression becomes

`3(-2)^2-2*(-2)+1 = 3*4+4+1 = 12+4+1 = 17`