Calculate y in y=x² When x Equals 10: Function Evaluation

Q: What does the exponent 2 actually mean?

The exponent 2 means multiply the base by itself. So $ x^2 $ means $ x \times x $, not $ 2 \times x $!

Q: Why isn't the answer 20 when x = 10?

Because $ x^2 $ doesn't mean 2 times x. It means x times x. So $ 10^2 = 10 \times 10 = 100 $, not $ 2 \times 10 = 20 $.

Q: How do I remember the difference between x² and 2x?

$ x^2 $ has the 2 as a superscript (small and raised) meaning "squared". $ 2x $ has the 2 in front meaning "two times x". The position matters!

Q: What if x was negative, like x = -10?

Then $ y = (-10)^2 = (-10) \times (-10) = 100 $. Remember: negative times negative equals positive, so the answer would still be 100!

Q: Can I use a calculator for this?

Yes! Most calculators have an x² button or you can type 10^2. But understanding that it means 10 times 10 helps you solve it by hand too.

Function Evaluation with Squared Variables

What is the value of y for the function?

$y=x^2$

of the point $x=10$ ?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

00:12 Let's calculate the exponent

00:16 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 $x=10$ ?

Step-by-step solution

To find the value of $y$ for the function $y = x^2$ at the point where $x = 10$ , we will follow these steps:

Step 1: Identify the function, which is $y = x^2$ .
Step 2: Substitute $x = 10$ into the function.
Step 3: Perform the calculation to find $y$ .

Now, let's work through each step:
Step 1: We have the function $y = x^2$ .
Step 2: Substitute $x = 10$ into the equation: $y = (10)^2$ .
Step 3: Calculate the result: $y = 10 \times 10 = 100$ .

Therefore, the value of $y$ for the function when $x = 10$ is $y = 100$ .

Final Answer

$y=100$

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace x with the given value in the function
Technique: Calculate $(10)^2 = 10 \times 10 = 100$
Check: Verify that $y = x^2$ gives $y = 100$ when $x = 10$ ✓

Common Mistakes

Avoid these frequent errors

Confusing exponent with multiplication
Don't calculate $x^2$ as $2 \times x = 2 \times 10 = 20$ ! The exponent 2 means multiply the base by itself, not by 2. Always calculate $x^2 = x \times x$ .

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 exponent 2 actually mean?

The exponent 2 means multiply the base by itself. So $x^2$ means $x \times x$ , not $2 \times x$ !

Why isn't the answer 20 when x = 10?

Because $x^2$ doesn't mean 2 times x. It means x times x. So $10^2 = 10 \times 10 = 100$ , not $2 \times 10 = 20$ .

How do I remember the difference between x² and 2x?

$x^2$ has the 2 as a superscript (small and raised) meaning "squared". $2x$ has the 2 in front meaning "two times x". The position matters!

What if x was negative, like x = -10?

Then $y = (-10)^2 = (-10) \times (-10) = 100$ . Remember: negative times negative equals positive, so the answer would still be 100!

Can I use a calculator for this?

Yes! Most calculators have an x² button or you can type 10^2. But understanding that it means 10 times 10 helps you solve it by hand too.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parabola Families questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime