Solve y = x² Function: Finding X When y = 16

Q: Why are there two answers when I solve $ x^2 = 16 $ ?

Because both positive and negative numbers give the same result when squared! $ 4^2 = 16 $ and $ (-4)^2 = 16 $, so both x = 4 and x = -4 are correct solutions.

Q: How do I remember to include both the positive and negative square root?

Use the ± symbol (plus-or-minus) when taking square roots! Write $ x = \pm\sqrt{16} $ to remind yourself that there are two solutions: one positive and one negative.

Q: What does the graph of $ y = x^2 $ look like at y = 16?

It's a U-shaped parabola that opens upward. At $ y = 16 $, the horizontal line crosses the parabola at two points: (4, 16) and (-4, 16), showing why there are two x-values!

Q: Can $ x^2 $ ever equal a negative number?

No! When you square any real number (positive or negative), the result is always positive or zero. So equations like $ x^2 = -9 $ have no real solutions.

Q: What if I get a decimal when taking the square root?

That's fine! For example, if $ x^2 = 20 $, then $ x = \pm\sqrt{20} = \pm2\sqrt{5} $ or approximately ±4.47. Always include both the positive and negative values.

Quadratic Functions with Both Positive and Negative Solutions

What is the value of X for the function?

$y=x^2$

of the point $y=16$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

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

00:12 Extract the root

00:15 When extracting a root there are 2 solutions, positive and negative

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

What is the value of X for the function?

$y=x^2$

of the point $y=16$ ?

Step-by-step solution

To solve this problem, let's find the steps required to determine $x$ when $y = 16$ in the function $y = x^2$ :

Step 1: Substitute the given $y$ into the equation to get $x^2 = 16$ .
Step 2: To solve $x^2 = 16$ , take the square root of both sides, remembering to include both positive and negative roots. This yields $x = \pm\sqrt{16}$ .
Step 3: Simplify to find $x = \pm4$ , which gives the solutions $x = 4$ and $x = -4$ .

Thus, the value(s) of $x$ that satisfy $y = 16$ in the function $y = x^2$ are $x = 4$ and $x = -4$ .

Therefore, the solution to the given problem is $x = 4, x = -4$ .

Final Answer

$x=4,x=-4$

Key Points to Remember

Essential concepts to master this topic

Rule: When solving $x^2 = a$ , always include both positive and negative roots
Technique: Take square root of both sides: $x = \pm\sqrt{16} = \pm4$
Check: Verify both solutions: $4^2 = 16$ and $(-4)^2 = 16$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution when taking square roots
Don't just write x = 4 when solving $x^2 = 16$ = missing half the answer! Squaring a negative number also gives a positive result. Always remember $x = \pm\sqrt{a}$ when solving $x^2 = a$ .

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 are there two answers when I solve $x^2 = 16$ ?

Because both positive and negative numbers give the same result when squared! $4^2 = 16$ and $(-4)^2 = 16$ , so both x = 4 and x = -4 are correct solutions.

How do I remember to include both the positive and negative square root?

Use the ± symbol (plus-or-minus) when taking square roots! Write $x = \pm\sqrt{16}$ to remind yourself that there are two solutions: one positive and one negative.

What does the graph of $y = x^2$ look like at y = 16?

It's a U-shaped parabola that opens upward. At $y = 16$ , the horizontal line crosses the parabola at two points: (4, 16) and (-4, 16), showing why there are two x-values!

Can $x^2$ ever equal a negative number?

No! When you square any real number (positive or negative), the result is always positive or zero. So equations like $x^2 = -9$ have no real solutions.

What if I get a decimal when taking the square root?

That's fine! For example, if $x^2 = 20$ , then $x = \pm\sqrt{20} = \pm2\sqrt{5}$ or approximately ±4.47. Always include both the positive and negative values.

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Solve y = x² Function: Finding X When y = 16

Quadratic Functions with Both Positive and Negative Solutions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why are there two answers when I solve $x^2 = 16$ ?

How do I remember to include both the positive and negative square root?

What does the graph of $y = x^2$ look like at y = 16?

Can $x^2$ ever equal a negative number?

What if I get a decimal when taking the square root?

🌟 Unlock Your Math Potential

More Questions

Parabola of the form y=x²

Solve y=x² When y=25: Finding the X-Value

Solve for X in y=x²: Finding X-Coordinates When y=8

Solve y=x² When y=4: Finding X-Coordinates

Solve y = x² Function: Finding X When y = 16

Quadratic Functions with Both Positive and Negative Solutions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why are there two answers when I solve x2=16 x^2 = 16 x2=16?

How do I remember to include both the positive and negative square root?

What does the graph of y=x2 y = x^2 y=x2 look like at y = 16?

Can x2 x^2 x2 ever equal a negative number?

What if I get a decimal when taking the square root?

🌟 Unlock Your Math Potential

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Parabola of the form y=x²

Solve y=x² When y=25: Finding the X-Value

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Why are there two answers when I solve $x^2 = 16$ ?

What does the graph of $y = x^2$ look like at y = 16?

Can $x^2$ ever equal a negative number?