Solve for 

y

.

9

y

2

–

12

y

+

4

=

0

*Write* *each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with* *commas.*

y

=

We are tasked with solving the quadratic equation:

\[
9y^2 - 12y + 4 = 0
\]

### Step 1: Check if the quadratic is factorable
We can try factoring the quadratic equation directly.

Looking at the equation:

\[
9y^2 - 12y + 4 = 0
\]

We check for a factorable form by recognizing that this is a perfect square trinomial:

\[
(3y - 2)^2 = 0
\]

### Step 2: Solve the factored form

Now that we have:

\[
(3y - 2)^2 = 0
\]

We can solve by taking the square root of both sides:

\[
3y - 2 = 0
\]

### Step 3: Isolate \( y \)

Solve for \( y \):

\[
3y = 2
\]

\[
y = \frac{2}{3}
\]

### Final Answer:

The solution is:

\[
y = \frac{2}{3}
\]

There is only one solution, and it is \( y = \frac{2}{3} \).

Would you like more details or have any questions?

---

Here are 5 related questions to expand on this topic:

1. How do you determine if a quadratic equation can be factored?
2. What are the steps involved in solving a quadratic using the quadratic formula?
3. What is a perfect square trinomial, and how can you recognize it?
4. How do you solve a quadratic equation that is not factorable?
5. Can a quadratic equation have more than one solution? If so, when?

**Tip:** Always check if a quadratic can be factored before using other methods, as factoring can save time.

Solve for y. 9y^2 - 12y + 4 = 0. Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. y =

Learn how to solve the quadratic equation 9y^2 - 12y + 4 = 0 using factoring. This detailed step-by-step guide explains perfect square trinomials and provides the solution y = 2/3, ideal for students in Grades 8-10.

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