Mastering Function Evaluation with g(x) = x² - 3x + 1

Have you ever encountered a math problem that left you scratching your head? You know the kind—where you’re told to find the value of a function at a certain point. It can feel a bit daunting at first, but don't worry! Let’s break it down together, step by step, using the function ( g(x) = x^2 - 3x + 1 ) as our guide.

First things first, let's tackle this with an example: What happens when we plug in ( x = 2 )? It’s like baking a cake—each ingredient must be mixed just right for a delicious result!

Step One: Substitute ( x ) with 2

To get started, we’ll substitute 2 into our function: [ g(2) = (2)^2 - 3(2) + 1 ] Can you picture it? You're replacing ( x ) like swapping out an ingredient in a recipe.

Step Two: Calculate ( (2)^2 )

Next, it’s time to calculate. What’s ( (2)^2 )? Ah, that’s an easy one! [ (2)^2 = 4 ] Simple enough, right? We’re off to a good start!

Step Three: Calculate ( -3(2) )

Now, let's tackle the next piece: [ -3(2) = -6 ] A little bit of multiplication action here! We’re digging deeper into our math ingredients.

Step Four: Combine All Parts

Here’s where the magic happens! Let’s combine everything we’ve found. We’ll plug those values into the original equation: [ g(2) = 4 - 6 + 1 ] See how it starts to take shape? Like crafting a beautiful piece of art, each part contributes to the whole.

Step Five: Simplify the Expression

And now, let’s simplify:

• First, do the subtraction: [ 4 - 6 = -2 ]
• Then add the last part: [ -2 + 1 = -1 ]

Voilà! The value of ( g(2) ) gives us (-1). This is where we finally reveal our cake—or in this case, our answer. It’s fascinating how simple calculations lead to a result that makes perfect sense, isn’t it?

In conclusion, when you substitute ( x = 2 ) into the function ( g(x) = x^2 - 3x + 1 ), you discover that ( g(2) = -1 ). It might seem tricky at first, but using these straightforward steps makes it much more manageable. And remember, the key to mastering any math concept is practice—so keep at it!

What do you think? Ready to tackle more functions or other equations? Who knows what interesting insights await as you continue this adventure in quantitative literacy!