Evaluate y = x² When x Equals 7: Point Existence Problem

Q: What does it mean to evaluate a function at a specific x-value?

Evaluating means finding the y-value when you know the x-value. Just substitute the given number for x and calculate the result!

Q: How do I know if a point exists on the function?

Every real number has a corresponding point on $ y = x^2 $! Since we can calculate $ 7^2 = 49 $, the point (7, 49) definitely exists.

Q: Why is the answer 49 and not 14?

Be careful with exponents! $ x^2 $ means x times itself, not x times 2. So $ 7^2 = 7 \times 7 = 49 $, not 7 × 2 = 14.

Q: What is the ordered pair for this point?

The ordered pair is (x, y) = (7, 49). The first number is always the x-coordinate, and the second number is the y-coordinate we calculated.

Q: Can I use a calculator for squaring numbers?

Yes! But make sure you understand that squaring means multiplying a number by itself. Practice mental math with smaller numbers like $ 3^2 = 9 $ and $ 5^2 = 25 $.

Quadratic Function Evaluation with Integer Values

Given the function:

$y=x^2$

Is there a point for ? $x=7$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Does the point exist?

00:04 Let's substitute appropriate values according to the given data, and solve to find the point

00:11 Let's calculate the power

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

Given the function:

$y=x^2$

Is there a point for ? $x=7$ ?

Step-by-step solution

The task is to find the value of $y$ when $x = 7$ for the function given by $y = x^2$ .

To solve this problem, we will perform the following steps:

Step 1: Substitute $x = 7$ into the function, resulting in the expression $y = 7^2$ .
Step 2: Calculate the square of 7, which is $7 \times 7 = 49$ .
Step 3: Hence, the value of $y$ is 49 when $x = 7$ .

The calculation shows that the point exists on the parabola described by $y = x^2$ and is represented by the ordered pair $(7, 49)$ .

Therefore, the solution to the problem, supported by calculations, is $y = 49$ .

Final Answer

$y=49$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace the variable with the given number value
Technique: Calculate $7^2 = 7 \times 7 = 49$ step by step
Check: Verify point (7, 49) lies on parabola $y = x^2$ ✓

Common Mistakes

Avoid these frequent errors

Confusing exponent with multiplication
Don't calculate $7^2$ as 7 × 2 = 14! This treats the exponent as multiplication instead of repeated multiplication. Always remember that $x^2$ means x × x, so $7^2 = 7 \times 7 = 49$ .

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 at a specific x-value?

Evaluating means finding the y-value when you know the x-value. Just substitute the given number for x and calculate the result!

How do I know if a point exists on the function?

Every real number has a corresponding point on $y = x^2$ ! Since we can calculate $7^2 = 49$ , the point (7, 49) definitely exists.

Why is the answer 49 and not 14?

Be careful with exponents! $x^2$ means x times itself, not x times 2. So $7^2 = 7 \times 7 = 49$ , not 7 × 2 = 14.

What is the ordered pair for this point?

The ordered pair is (x, y) = (7, 49). The first number is always the x-coordinate, and the second number is the y-coordinate we calculated.

Can I use a calculator for squaring numbers?

Yes! But make sure you understand that squaring means multiplying a number by itself. Practice mental math with smaller numbers like $3^2 = 9$ and $5^2 = 25$ .

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