Calculate y = x² When x = 12: Function Evaluation Practice

Q: What does the little 2 above the x mean?

The exponent 2 means you multiply x by itself. So $ x^2 $ = x × x. When x = 12, we get $ 12^2 $ = 12 × 12 = 144.

Q: Is there a faster way to calculate 12 squared?

Yes! You can use patterns: $ 12^2 = (10 + 2)^2 = 100 + 40 + 4 = 144 $. Or simply memorize that $ 12^2 = 144 $ since it's a perfect square.

Q: Why isn't the answer just 12?

Because we're not solving for x! We're evaluating the function y = $ x^2 $ when x = 12. This means we substitute 12 into the function and calculate the result.

Q: What if x was negative, like x = -12?

Great question! $ (-12)^2 = (-12) \times (-12) = 144 $. The result is still positive because negative times negative equals positive!

Function Evaluation with Quadratic Expressions

What is the value of y for the function?

$y=x^2$

of the point $x=12$ ?

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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 We'll substitute appropriate values according to the given data, and solve for X

00:14 Let's calculate the power

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 $x=12$ ?

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Apply the appropriate formula by substituting the given value.
Step 3: Perform the calculation to find the solution.

Let's work through each step:

Step 1: The function is given by $y = x^2$ and the value of $x$ is 12.

Step 2: Substitute $x = 12$ into the function. We have:

$y = 12^2$ .

Step 3: Calculate the square of 12:

$12^2 = 144$ .

Therefore, the value of $y$ at the point $x = 12$ is $y = 144$ .

Comparing this with the multiple-choice answers, the correct choice is:

Choice 4: $y = 144$ .

Thus, the final answer is $y = 144$ .

Final Answer

$y=144$

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace the variable with the given numeric value
Technique: Calculate $12^2 = 12 \times 12 = 144$
Check: Verify by confirming $y = 12^2$ equals 144 ✓

Common Mistakes

Avoid these frequent errors

Confusing exponents with multiplication
Don't calculate $x^2$ as $2x = 2 \times 12 = 24$ ! This confuses the exponent 2 with multiplication by 2, giving a completely wrong result. Always remember that $x^2$ means x times itself.

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

What does the little 2 above the x mean?

The exponent 2 means you multiply x by itself. So $x^2$ = x × x. When x = 12, we get $12^2$ = 12 × 12 = 144.

Is there a faster way to calculate 12 squared?

Yes! You can use patterns: $12^2 = (10 + 2)^2 = 100 + 40 + 4 = 144$ . Or simply memorize that $12^2 = 144$ since it's a perfect square.

Why isn't the answer just 12?

Because we're not solving for x! We're evaluating the function y = $x^2$ when x = 12. This means we substitute 12 into the function and calculate the result.

What if x was negative, like x = -12?

Great question! $(-12)^2 = (-12) \times (-12) = 144$ . The result is still positive because negative times negative equals positive!

How do I know I didn't make a calculation error?

Double-check your multiplication: 12 × 12. You can break it down: $12 \times 12 = 12 \times 10 + 12 \times 2 = 120 + 24 = 144$ .

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