Verify Point (6,36) on the Function y = x²: Coordinate Check

Q: What does it mean for a function to pass through a point?

A function passes through a point $ (x, y) $ when you substitute the x-value into the function and get exactly the y-value from that point. It's like the point sits perfectly on the graph!

Q: Do I always substitute the x-value first?

Yes! Always start with the x-coordinate. Substitute it into the function equation, then check if your calculated result matches the y-coordinate.

Q: What if my calculation doesn't match the y-coordinate?

Then the function does not pass through that point! For example, if $ y = x^2 $ and point (5, 30), we get $ 5^2 = 25 ≠ 30 $, so it doesn't pass through.

Q: Can a point be on multiple functions?

Absolutely! The point (6, 36) lies on $ y = x^2 $, but it could also be on other functions like $ y = 6x $. Each function needs to be checked separately.

Q: Why is this skill important?

Checking if points lie on functions helps you verify solutions, understand graphs, and solve real-world problems. It's like double-checking your work in algebra!

Function Evaluation with Coordinate Verification

Does the function $y=x^2$ pass through the point where y = 36 and x = 6?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Does the point exist?

00:05 Let's substitute appropriate values according to the given data, and solve to find the point

00:11 Let's calculate the exponent

00:15 We can see that the point exists

00:20 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

Does the function $y=x^2$ pass through the point where y = 36 and x = 6?

Step-by-step solution

To determine if the function $y = x^2$ passes through the point $(6, 36)$ , follow these steps:

Step 1: Identify the given point and function. We have $x = 6$ and we need to check if $y = 36$ when $y = x^2$ .
Step 2: Substitute $x = 6$ in the function $y = x^2$ :
$y = 6^2 = 36$ .
Step 3: Compare the calculated $y$ value (36) to the given value (36).

Since the calculated value of $y$ is equal to the given value, the function $y = x^2$ indeed passes through the point $(6, 36)$ .

Therefore, the answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace x with given value in the function equation
Calculation: Compute $y = 6^2 = 36$ using the function
Verification: Compare calculated y-value (36) with given y-coordinate (36) ✓

Common Mistakes

Avoid these frequent errors

Checking if x equals y instead of substituting into function
Don't just compare x = 6 and y = 36 to see if they're equal = wrong approach! This ignores the function relationship completely. Always substitute the x-value into the function and check if the result matches the y-coordinate.

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 it mean for a function to pass through a point?

A function passes through a point $(x, y)$ when you substitute the x-value into the function and get exactly the y-value from that point. It's like the point sits perfectly on the graph!

Do I always substitute the x-value first?

Yes! Always start with the x-coordinate. Substitute it into the function equation, then check if your calculated result matches the y-coordinate.

What if my calculation doesn't match the y-coordinate?

Then the function does not pass through that point! For example, if $y = x^2$ and point (5, 30), we get $5^2 = 25 ≠ 30$ , so it doesn't pass through.

Can a point be on multiple functions?

Absolutely! The point (6, 36) lies on $y = x^2$ , but it could also be on other functions like $y = 6x$ . Each function needs to be checked separately.

Why is this skill important?

Checking if points lie on functions helps you verify solutions, understand graphs, and solve real-world problems. It's like double-checking your work in algebra!

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