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

Q: Why are there two answers when f(x) = 9?

Because two different x-values give the same output! Both $ 3^2 = 9 $ and $ (-3)^2 = 9 $. This happens because squaring eliminates the sign difference.

Q: What if the question asks for just one answer?

Read carefully! This question asks for the missing value and gives multiple choice options. Since both 3 and -3 work, you need to select the option that includes both solutions.

Q: Can I check my work by plugging numbers back in?

Absolutely! Always verify: $ f(3) = 3^2 = 9 ✓ $ and $ f(-3) = (-3)^2 = 9 ✓ $. If both give you 9, you're correct!

Q: Why isn't f(9) one of the correct answers?

Because $ f(9) = 9^2 = 81 $, not 9! The question asks what input gives output 9, not what happens when the input is 9.

Quadratic Functions with Two-Solution Problems

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=9$

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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

00:12 Extract the root

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

00:20 These are the 2 points

00:25 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:

$f(x)=x^2$

$f(?)=9$

Step-by-step solution

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

Step 1: Set up the equation $x^2 = 9$ .
Step 2: Solve for $x$ by taking the square root of both sides.
Step 3: Choose the correct answer from the given options.

Now, let's work through each step:
Step 1: We set $x^2 = 9$ .
Step 2: Solving for $x$ , we take the square root of both sides: $x = \pm \sqrt{9}$ .
Step 3: This yields two solutions: $x = 3$ and $x = -3$ .

Comparing these values with the given choices:

Choice 1: $f(3)$ corresponds to $x = 3$ .
Choice 3: $f(-3)$ corresponds to $x = -3$ .

Both choices $f(3)$ and $f(-3)$ are correct, leading us to select the combined choice: Answer A+C.

Final Answer

Answer A+C

Key Points to Remember

Essential concepts to master this topic

Square Root Property: When $x^2 = a$ , then $x = \pm\sqrt{a}$
Technique: Set up $x^2 = 9$ , then $x = \pm 3$
Check: Verify both solutions: $3^2 = 9$ and $(-3)^2 = 9$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution
Don't only write x = 3 when solving x² = 9 = missing half the answer! Square roots always have two solutions because both positive and negative numbers square to give positive results. Always write x = ±√9 = ±3.

Practice Quiz

Test your knowledge with interactive questions

What is the value of y for the function?

$$ y=x^2 $$

of the point $$ x=2 $$ ?

FAQ

Everything you need to know about this question

Why are there two answers when f(x) = 9?

Because two different x-values give the same output! Both $3^2 = 9$ and $(-3)^2 = 9$ . This happens because squaring eliminates the sign difference.

How do I know if I need the ± symbol?

Use ± whenever you take the square root of both sides of an equation. If you see $x^2 = \text{number}$ , then $x = \pm\sqrt{\text{number}}$ .

What if the question asks for just one answer?

Read carefully! This question asks for the missing value and gives multiple choice options. Since both 3 and -3 work, you need to select the option that includes both solutions.

Can I check my work by plugging numbers back in?

Absolutely! Always verify: $f(3) = 3^2 = 9 ✓$ and $f(-3) = (-3)^2 = 9 ✓$ . If both give you 9, you're correct!

Why isn't f(9) one of the correct answers?

Because $f(9) = 9^2 = 81$ , not 9! The question asks what input gives output 9, not what happens when the input is 9.

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