Evaluate y = x² When x = 7: Function Value Calculation

Q: Why isn't the answer -49 if we're squaring?

Great question! When we square a positive number like 7, we get a positive result. $ 7^2 = 7 \times 7 = 49 $. Only when you square a negative number do you still get positive: $ (-7)^2 = 49 $.

Q: What does the notation y = x² actually mean?

The notation $ y = x^2 $ is a function that tells you the relationship between x and y. For any x-value you put in, y equals that number multiplied by itself.

Q: How do I know which value to substitute?

Look for phrases like "when x = 7" or "at the point x = 7". This tells you exactly which number to substitute for the variable in your function.

Q: What if x was a negative number instead?

If x = -7, then $ y = (-7)^2 = (-7) \times (-7) = 49 $. Remember: negative × negative = positive, so you'd still get 49!

Q: Is there a faster way to calculate 7²?

You can memorize common squares! Perfect squares like $ 1^2=1, 2^2=4, 3^2=9, ..., 10^2=100 $ are worth knowing by heart to speed up your work.

Function Evaluation with Quadratic Expressions

What is the value of y for the function?

$y=x^2$

of the point $x=7$ ?

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Step-by-step video solution

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00:00 Set up and solve

00:03 We'll substitute appropriate values according to the given data, and solve for X

00:11 Let's calculate the exponent

00:15 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 $x=7$ ?

Step-by-step solution

To find the value of $y$ when $x = 7$ in the function $y = x^2$ , we will follow these straightforward steps:

Step 1: Substitute $x = 7$ into the function. Therefore, $y = (7)^2$ .
Step 2: Calculate the value of $7^2$ . The expression $7^2$ means $7 \times 7$ .
Step 3: Perform the multiplication. $7 \times 7 = 49$ .

Thus, when $x = 7$ , the value of $y$ is $49$ .

Therefore, the value of $y$ at $x = 7$ is $y = 49$ .

Final Answer

$y=49$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace variable with given value in function
Technique: Calculate $7^2 = 7 \times 7 = 49$
Check: Verify by substituting back: $y = (7)^2 = 49$ ✓

Common Mistakes

Avoid these frequent errors

Confusing signs with exponents
Don't think $x^2$ can equal negative values for positive x = wrong sign! A squared positive number is always positive. Always remember: positive × positive = positive, so $7^2 = 49$ , not -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

Why isn't the answer -49 if we're squaring?

Great question! When we square a positive number like 7, we get a positive result. $7^2 = 7 \times 7 = 49$ . Only when you square a negative number do you still get positive: $(-7)^2 = 49$ .

What does the notation y = x² actually mean?

The notation $y = x^2$ is a function that tells you the relationship between x and y. For any x-value you put in, y equals that number multiplied by itself.

How do I know which value to substitute?

Look for phrases like "when x = 7" or "at the point x = 7". This tells you exactly which number to substitute for the variable in your function.

What if x was a negative number instead?

If x = -7, then $y = (-7)^2 = (-7) \times (-7) = 49$ . Remember: negative × negative = positive, so you'd still get 49!

Is there a faster way to calculate 7²?

You can memorize common squares! Perfect squares like $1^2=1, 2^2=4, 3^2=9, ..., 10^2=100$ are worth knowing by heart to speed up your work.

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