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The image shows a math problem related to a **non-linear demand and supply function**. Here's the content extracted from the image:

### Functions:
- Supply function: \( P_s = Q^2 + 6Q + 9 \)
- Demand function: \( P_d = Q^2 - 10Q + 25 \)

### Questions:
- **(a)** Draw the graph of the functions for the interval \( Q = 0 \) to \( Q = 5 \).
- **(b)** Find the equilibrium point for price and quantity.

#### Let's break it down:

1. **(a) Graph the Functions:**
   You are asked to graph the supply and demand functions within the interval \( Q = 0 \) to \( Q = 5 \). You can plot the two functions and observe where they intersect within this interval.

2. **(b) Find the Equilibrium Point:**
   The equilibrium occurs when the quantity supplied equals the quantity demanded, which means setting \( P_s = P_d \), and solving for \( Q \).

### Solving for the equilibrium point:
Equating the two functions:

\[
Q^2 + 6Q + 9 = Q^2 - 10Q + 25
\]

Simplifying:

\[
6Q + 9 = -10Q + 25
\]
\[
16Q = 16
\]
\[
Q = 1
\]

Now substitute \( Q = 1 \) into either function to find the price:

For \( P_s \):
\[
P_s = (1)^2 + 6(1) + 9 = 1 + 6 + 9 = 16
\]

Therefore, the equilibrium point is \( Q = 1 \) and \( P = 16 \).

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Would you like a detailed graph for the two functions or further explanations on this? Let me know if you have any questions.

Here are 5 related questions you could explore:
1. How do quadratic functions differ from linear functions in economics?
2. What is the significance of equilibrium in supply and demand models?
3. Can equilibrium points exist outside the specified interval?
4. How does shifting the demand curve affect equilibrium?
5. What does a higher price elasticity mean for demand and supply?

**Tip:** The intersection of supply and demand functions determines the equilibrium price and quantity in the market.

Ps = Q^2 + 6Q + 9 and Pd = Q^2 - 10Q + 25. (a) Draw the graph of the functions for the interval Q = 0 to Q = 5. (b) Find the equilibrium point for price and quantity.

Learn how to solve a non-linear supply and demand function using quadratic equations. This problem explores equilibrium points between Ps = Q^2 + 6Q + 9 and Pd = Q^2 - 10Q + 25, suitable for Grades 10-12 students.

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