Solve y = x² When y = 36: Finding the X-Coordinate

Q: Why do we get two answers instead of just one?

Because both positive and negative numbers give the same result when squared! Since $ 6^2 = 36 $ and $ (-6)^2 = 36 $, we need both solutions: x = 6 and x = -6.

Q: What does the ± symbol mean exactly?

The plus-minus symbol (±) is shorthand for two separate solutions. When we write $ x = ±6 $, it means x = +6 OR x = -6.

Q: How do I remember to include both solutions?

Think about it this way: squaring always makes numbers positive, so any positive result could have come from either a positive or negative original number. Always use ± when taking square roots!

Q: Can I just write x = 6 if the problem asks for 'the' solution?

No! Quadratic equations typically have two solutions unless specifically stated otherwise. Both $ x = 6 $ and $ x = -6 $ are equally valid answers.

Q: What if the number under the square root was negative?

Great question! If we had something like $ x^2 = -36 $, there would be no real solutions because no real number squared gives a negative result.

Q: How can I check my work quickly?

Simply square both of your answers and see if you get the original y-value. For this problem: $ 6^2 = 36 ✓ $ and $ (-6)^2 = 36 ✓ $

Quadratic Equations with Plus-Minus Solutions

What is the value of X for the function?

$y=x^2$

of the point $y=36$ ?

❤️ 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

00:03 Substitute appropriate values according to the given data, and solve for X

00:11 Extract the root

00:16 When extracting a root there are 2 solutions, positive and negative

00:19 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 X for the function?

$y=x^2$

of the point $y=36$ ?

Step-by-step solution

To solve the problem, we will proceed with the following steps:

Identify the provided equation and condition.
Apply the square root property to solve the equation.
Verify the solution with the given choices.

Step-by-step solution:

Step 1: Substitute $y = 36$ into the equation $y = x^2$ , which gives:

$x^2 = 36$

Step 2: Solve for $x$ by taking the square root of both sides. Using the square root property, we have:

$x = \pm \sqrt{36}$

Since the square root of 36 is 6, we find that:

$x = \pm 6$

Therefore, the solutions to the equation are $x = 6$ and $x = -6$ .

Thus, the value of $x$ for $y = 36$ in the function $y = x^2$ is $x = \pm 6$ .

Final Answer

$x=\pm6$

Key Points to Remember

Essential concepts to master this topic

Square Root Property: When x² = k, then x = ±√k
Technique: Substitute y = 36 to get x² = 36, then x = ±6
Check: Verify both solutions: (6)² = 36 and (-6)² = 36 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution when taking square roots
Don't write x = 6 as the only answer when solving x² = 36! This misses half the solution because both positive and negative numbers square to give positive results. Always include the ± symbol: x = ±6.

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 do we get two answers instead of just one?

Because both positive and negative numbers give the same result when squared! Since $6^2 = 36$ and $(-6)^2 = 36$ , we need both solutions: x = 6 and x = -6.

What does the ± symbol mean exactly?

The plus-minus symbol (±) is shorthand for two separate solutions. When we write $x = ±6$ , it means x = +6 OR x = -6.

How do I remember to include both solutions?

Think about it this way: squaring always makes numbers positive, so any positive result could have come from either a positive or negative original number. Always use ± when taking square roots!

Can I just write x = 6 if the problem asks for 'the' solution?

No! Quadratic equations typically have two solutions unless specifically stated otherwise. Both $x = 6$ and $x = -6$ are equally valid answers.

What if the number under the square root was negative?

Great question! If we had something like $x^2 = -36$ , there would be no real solutions because no real number squared gives a negative result.

How can I check my work quickly?

Simply square both of your answers and see if you get the original y-value. For this problem: $6^2 = 36 ✓$ and $(-6)^2 = 36 ✓$

🌟 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