Evaluate y = x² When x = 6: Finding the Output Value

Q: What does x² actually mean?

x² means x times x, not x times 2! So when x = 6, we calculate $ 6^2 = 6 \times 6 = 36 $, not 6 × 2 = 12.

Q: How do I substitute the value correctly?

Replace every x in the function with the given value. For $ y = x^2 $ when x = 6, write $ y = (6)^2 $, then calculate the result.

Q: What if x was negative, like x = -6?

Even with negative values, $ (-6)^2 = (-6) \times (-6) = 36 $. Remember: negative times negative equals positive!

Q: Can I use a calculator for this?

Absolutely! But make sure you understand that $ 6^2 $ on your calculator gives the same result as 6 × 6. Both methods should give you 36.

Function Evaluation with Quadratic Expressions

What is the value of y for the function?

$y=x^2$

of the point $x=6$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

00:03 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 $x=6$ ?

Step-by-step solution

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

Step 1: Identify the value given for $x$ .
Step 2: Substitute the given $x$ value into the function.
Step 3: Calculate the resulting value for $y$ .

Now, let's work through each step:
Step 1: The problem states that $x = 6$ .
Step 2: Using the function $y = x^2$ , we substitute $x = 6$ .
Step 3: Perform the calculation: $y = 6^2$ .

Calculating $6^2$ , we get $36$ .
Therefore, for the function $y = x^2$ , when $x = 6$ , the value of $y$ is $y = 36$ .

Final Answer

$y=36$

Key Points to Remember

Essential concepts to master this topic

Rule: Replace every x with the given value in parentheses
Technique: Calculate $6^2 = 6 \times 6 = 36$ step by step
Check: Verify by substituting: when x = 6, $y = 6^2 = 36$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying x by the exponent instead of squaring
Don't calculate $6^2$ as 6 × 2 = 12! This treats the exponent as multiplication instead of repeated multiplication. Always remember that $x^2$ means x × x, so $6^2 = 6 \times 6 = 36$ .

Practice Quiz

Test your knowledge with interactive questions

What is the value of y for the function?

$$ y=x^2 $$

of the point $$ x=2 $$ ?

FAQ

Everything you need to know about this question

What does x² actually mean?

x² means x times x, not x times 2! So when x = 6, we calculate $6^2 = 6 \times 6 = 36$ , not 6 × 2 = 12.

Why isn't the answer negative?

When you square any real number (positive or negative), the result is always positive! Since $6^2 = 6 \times 6 = 36$ , we get a positive answer.

How do I substitute the value correctly?

Replace every x in the function with the given value. For $y = x^2$ when x = 6, write $y = (6)^2$ , then calculate the result.

What if x was negative, like x = -6?

Even with negative values, $(-6)^2 = (-6) \times (-6) = 36$ . Remember: negative times negative equals positive!

Can I use a calculator for this?

Absolutely! But make sure you understand that $6^2$ on your calculator gives the same result as 6 × 6. Both methods should give you 36.

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Evaluate y = x² When x = 6: Finding the Output Value

Function Evaluation with Quadratic Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does x² actually mean?

Why isn't the answer negative?

How do I substitute the value correctly?

What if x was negative, like x = -6?

Can I use a calculator for this?

🌟 Unlock Your Math Potential

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