Solve Quadratic Function: Finding x When f(x) = x² Equals 81

Q: Why are there two answers when I solve $ x^2 = 81 $ ?

Because both positive and negative numbers give the same result when squared! Think about it: $ 9^2 = 9 \times 9 = 81 $ and $ (-9)^2 = (-9) \times (-9) = 81 $.

Q: How do I know which solution to pick from the answer choices?

Look carefully at the given options! In this problem, only $ f(-9) $ appears in the choices, so that's your answer. Sometimes both solutions might be listed, sometimes just one.

Q: What if the number under the square root isn't a perfect square?

You can still solve it! For example, $ x^2 = 50 $ gives $ x = \pm\sqrt{50} $. You might need to simplify the radical or use a calculator for decimal approximations.

Q: Can I check my answer by plugging it back into the original function?

Absolutely! That's the best way to verify. If $ f(x) = x^2 $ and you think $ x = -9 $, then check: $ f(-9) = (-9)^2 = 81 $ ✓

Q: Why is $ f(27) $ wrong when 27 is close to the square root?

Close isn't good enough in math! $ f(27) = 27^2 = 729 $, which is much larger than 81. Always calculate exactly rather than guessing based on proximity.

Quadratic Functions with Square Root Solutions

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=81$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and solve

00:04 We'll substitute appropriate values according to the given data, and solve for X

00:13 Extract the root

00:17 When extracting a root there are 2 solutions, positive and negative

00:22 These are the 2 points

00:29 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

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=81$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Set up the equation $x^2 = 81$ .
Step 2: Solve for $x$ by taking the square root of both sides.
Step 3: Confirm that the solutions are integers provided in the choices.

Now, let's work through each step:
Step 1: The problem gives us the function $f(x) = x^2$ and asks us to find values of $x$ such that $f(x) = 81$
Step 2: Solving $x^2 = 81$ , we take the square root of both sides to get $x = \pm \sqrt{81}$ .
Step 3: Compute $\sqrt{81} = 9$ , which gives us $x = 9$ or $x = -9$ . Therefore, the solutions are $x = 9$ and $x = -9$ .

Considering the given choices, we can identify that $f(-9) = 81$ , which corresponds to choice 1 in the problem.

Therefore, the solution to the problem is $\boldsymbol{f(-9)}$ .

Final Answer

$f(-9)$

Key Points to Remember

Essential concepts to master this topic

Rule: When solving $x^2 = k$ , remember both positive and negative roots
Technique: $x^2 = 81$ gives $x = \pm\sqrt{81} = \pm 9$
Check: Verify both solutions: $(-9)^2 = 81$ and $(9)^2 = 81$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution
Don't solve $x^2 = 81$ and only write $x = 9$ = missing half the answer! Since any number squared gives a positive result, both 9 and -9 work. Always remember $x = \pm\sqrt{k}$ when solving $x^2 = k$ .

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 $x^2 = 81$ ?

Because both positive and negative numbers give the same result when squared! Think about it: $9^2 = 9 \times 9 = 81$ and $(-9)^2 = (-9) \times (-9) = 81$ .

How do I know which solution to pick from the answer choices?

Look carefully at the given options! In this problem, only $f(-9)$ appears in the choices, so that's your answer. Sometimes both solutions might be listed, sometimes just one.

What if the number under the square root isn't a perfect square?

You can still solve it! For example, $x^2 = 50$ gives $x = \pm\sqrt{50}$ . You might need to simplify the radical or use a calculator for decimal approximations.

Can I check my answer by plugging it back into the original function?

Absolutely! That's the best way to verify. If $f(x) = x^2$ and you think $x = -9$ , then check: $f(-9) = (-9)^2 = 81$ ✓

Why is $f(27)$ wrong when 27 is close to the square root?

Close isn't good enough in math! $f(27) = 27^2 = 729$ , which is much larger than 81. Always calculate exactly rather than guessing based on proximity.

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Solve Quadratic Function: Finding x When f(x) = x² Equals 81

Quadratic Functions with Square Root 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 $x^2 = 81$ ?

How do I know which solution to pick from the answer choices?

What if the number under the square root isn't a perfect square?

Can I check my answer by plugging it back into the original function?

Why is $f(27)$ wrong when 27 is close to the square root?

🌟 Unlock Your Math Potential

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Solve Quadratic Function f(x) = x²: Finding Input When f(x) = 9

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Solve Quadratic Function: Finding x When f(x) = x² Equals 81

Quadratic Functions with Square Root 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=81 x^2 = 81 x2=81?

How do I know which solution to pick from the answer choices?

What if the number under the square root isn't a perfect square?

Can I check my answer by plugging it back into the original function?

Why is f(27) f(27) f(27) wrong when 27 is close to the square root?

🌟 Unlock Your Math Potential

More Questions

Parabola of the form y=x²

Find the Square Perimeter Function: Side Length 'a' Expression

Solve f(x) = x²: Finding the Function Point Where f(x) = 64

Solve Quadratic Function f(x) = x²: Finding Input When f(x) = 9

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

Why are there two answers when I solve $x^2 = 81$ ?

Why is $f(27)$ wrong when 27 is close to the square root?