The given equation is \( y = \frac{2}{3} (x+4)(x+3) \). 

To better understand this equation, we can expand it and put it in standard quadratic form, \( y = ax^2 + bx + c \).

### Step 1: Expand the binomials
We first expand \( (x+4)(x+3) \) using the distributive property (FOIL method):

\[
(x + 4)(x + 3) = x^2 + 3x + 4x + 12 = x^2 + 7x + 12
\]

### Step 2: Multiply by \( \frac{2}{3} \)
Now, multiply the expanded expression by \( \frac{2}{3} \):

\[
y = \frac{2}{3}(x^2 + 7x + 12)
\]

Distribute \( \frac{2}{3} \) to each term:

\[
y = \frac{2}{3}x^2 + \frac{14}{3}x + 8
\]

### Final Result:
The equation in standard quadratic form is:

\[
y = \frac{2}{3}x^2 + \frac{14}{3}x + 8
\]

Would you like a breakdown of how to find key features like the vertex, roots, or other properties of this quadratic?

Here are some related questions for further exploration:
1. How do you find the vertex of the quadratic function?
2. How can you determine the x-intercepts (roots) of this function?
3. What does the graph of this quadratic look like?
4. How do you find the axis of symmetry of the quadratic?
5. What is the significance of the leading coefficient \( \frac{2}{3} \)?

**Tip:** When multiplying a binomial by a fraction, distribute the fraction to each term to avoid mistakes.

This lesson explains how to expand and simplify the quadratic equation y = 2/3 (x+4)(x+3). Learn key algebraic concepts, including binomial expansion and converting the equation into standard form y = ax^2 + bx + c. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation