Evaluate y = x² Function: Finding Point at x = 11

Q: What does it mean to evaluate a function?

Function evaluation means finding the y-value (output) when you know the x-value (input). Just substitute the given x-value into the function equation!

Q: How do I calculate 11² without a calculator?

Break it down: $ 11^2 = 11 × 11 $. Think of it as $ (10 + 1) × (10 + 1) = 100 + 10 + 10 + 1 = 121 $, or just memorize that 11² = 121!

Q: Does every x-value have a point on y = x²?

Yes! For the function $ y = x^2 $, you can substitute any real number for x and get a corresponding y-value. This creates a point (x, y) on the parabola.

Q: What if I got 110 as my answer?

You might have calculated $ 11 × 10 $ instead of $ 11 × 11 $. Remember: $ x^2 $ means x times x, not x times 10!

Q: How can I check if (11, 121) is really on the curve?

Substitute both values: does $ 121 = 11^2 $? Yes! Since $ 11^2 = 121 $, the point (11, 121) definitely lies on the parabola $ y = x^2 $.

Quadratic Functions with Function Evaluation

Given the function:

$y=x^2$

Is there a point for ? $x=11$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Does the point exist?

00:03 Let's substitute appropriate values according to the given data, and solve to find the point

00:11 Let's calculate the exponent

00:14 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

Given the function:

$y=x^2$

Is there a point for ? $x=11$ ?

Step-by-step solution

To solve this problem, we will calculate the value of $y$ for the given function $y = x^2$ when $x = 11$ .

Here are the steps to find the solution:

Step 1: Substitute $x = 11$ into the function equation.
Step 2: Calculate $y = 11^2$ .

Let's work through these steps:

Step 1: By substituting $x = 11$ , the function becomes $y = 11^2$ .

Step 2: Calculate the value:

$11^2 = 11 \times 11 = 121$

Therefore, for $x = 11$ , the value of $y$ is $121$ , meaning the point $(11, 121)$ does exist on the function $y = x^2$ .

The correct answer from the given choices is $y = 121$ , which corresponds to choice id "3".

Final Answer

$y=121$

Key Points to Remember

Essential concepts to master this topic

Function Evaluation: Substitute the given x-value into the function equation
Technique: Replace x with 11: $y = 11^2 = 121$
Check: Verify that 11 × 11 = 121 creates point (11, 121) ✓

Common Mistakes

Avoid these frequent errors

Calculating exponents incorrectly
Don't confuse $11^2$ with 11 × 2 = 22! This gives completely wrong y-values. Always remember that $x^2$ means x × x, so $11^2 = 11 × 11 = 121$ .

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 to evaluate a function?

Function evaluation means finding the y-value (output) when you know the x-value (input). Just substitute the given x-value into the function equation!

How do I calculate 11² without a calculator?

Break it down: $11^2 = 11 × 11$ . Think of it as $(10 + 1) × (10 + 1) = 100 + 10 + 10 + 1 = 121$ , or just memorize that 11² = 121!

Does every x-value have a point on y = x²?

Yes! For the function $y = x^2$ , you can substitute any real number for x and get a corresponding y-value. This creates a point (x, y) on the parabola.

What if I got 110 as my answer?

You might have calculated $11 × 10$ instead of $11 × 11$ . Remember: $x^2$ means x times x, not x times 10!

How can I check if (11, 121) is really on the curve?

Substitute both values: does $121 = 11^2$ ? Yes! Since $11^2 = 121$ , the point (11, 121) definitely lies on the parabola $y = x^2$ .

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