Evaluate y = x² When x = 2: Function Value Problem

Q: Do I need to show parentheses when substituting positive numbers?

While not required for positive numbers, it's a great habit to use parentheses like $ y = (2)^2 $. This helps you avoid mistakes when working with negative numbers later!

Q: What's the difference between x² and (x)²?

For positive numbers, there's no difference: both $ 2^2 $ and $ (2)^2 $ equal 4. But for negative numbers, $ -2^2 = -4 $ while $ (-2)^2 = 4 $!

Q: How do I know which answer choice is correct?

Always calculate first, then compare to the choices. For $ x = 2 $ in $ y = x^2 $, you get $ y = 4 $ (positive), so negative answers like -4 or -8 are automatically wrong.

Q: Why isn't the answer 8 when x = 2?

That would be $ 2 \times 4 = 8 $, but we need $ 2^2 $ which means 2 times itself: $ 2 \times 2 = 4 $. The exponent tells you how many times to multiply the base by itself!

Q: Can I use a calculator for this?

You can, but mental math is faster for simple squares! Know these by heart: $ 1^2 = 1 $, $ 2^2 = 4 $, $ 3^2 = 9 $, $ 4^2 = 16 $, $ 5^2 = 25 $.

Function Evaluation with Substitution Method

What is the value of y for the function?

$y=x^2$

of the point $x=2$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

00:04 Let's substitute appropriate values according to the given data, and solve for X

00:14 Let's calculate the exponent

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the value of y for the function?

$y=x^2$

of the point $x=2$ ?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Substitute the given value of $x$ into the equation.
Step 2: Perform the calculation to find $y$ .

Now, let's work through each step:
Step 1: The given equation is $y = x^2$ . We need to substitute $x = 2$ into this equation.

Step 2: Substitute to get $y = (2)^2$ . Calculate $2 \times 2 = 4$ .

Therefore, the value of $y$ when $x = 2$ is $y = 4$ .

Hence, the solution to the problem is $y = 4$ .

Final Answer

$y=4$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace the variable with the given value exactly
Technique: For $y = x^2$ when $x = 2$ , calculate $(2)^2 = 4$
Check: Verify $y = 4$ by confirming $2 \times 2 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to use parentheses around negative values
Don't substitute x = -2 as y = -2² = -4! This gives the wrong sign because you're only squaring the 2, not the negative. Always use parentheses: y = (-2)² = 4.

Practice Quiz

Test your knowledge with interactive questions

Complete:

The missing value of the function point:

$$ f(x)=x^2 $$

$$ f(?)=16 $$

FAQ

Everything you need to know about this question

Do I need to show parentheses when substituting positive numbers?

While not required for positive numbers, it's a great habit to use parentheses like $y = (2)^2$ . This helps you avoid mistakes when working with negative numbers later!

What's the difference between x² and (x)²?

For positive numbers, there's no difference: both $2^2$ and $(2)^2$ equal 4. But for negative numbers, $-2^2 = -4$ while $(-2)^2 = 4$ !

How do I know which answer choice is correct?

Always calculate first, then compare to the choices. For $x = 2$ in $y = x^2$ , you get $y = 4$ (positive), so negative answers like -4 or -8 are automatically wrong.

Why isn't the answer 8 when x = 2?

That would be $2 \times 4 = 8$ , but we need $2^2$ which means 2 times itself: $2 \times 2 = 4$ . The exponent tells you how many times to multiply the base by itself!

Can I use a calculator for this?

You can, but mental math is faster for simple squares! Know these by heart: $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , $4^2 = 16$ , $5^2 = 25$ .

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