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The 9th and 10th questions from the image relate to finding the maximum height of a quadratic function:

**9th question:**
The quadratic function is \( f(x) = -5x^2 + 35x + 5 \). You need to find the maximum height of the rocket in flight.

To find the maximum height of a quadratic function \( f(x) = ax^2 + bx + c \), you can use the formula for the vertex \( x = -\frac{b}{2a} \), where the vertex gives the maximum point if \( a \) is negative.

For this function:
- \( a = -5 \)
- \( b = 35 \)

The \( x \)-coordinate of the vertex (where the maximum height occurs) is:
\[
x = -\frac{35}{2(-5)} = 3.5
\]

Now, substitute \( x = 3.5 \) into the original equation to find the maximum height:
\[
f(3.5) = -5(3.5)^2 + 35(3.5) + 5 = 66.25
\]

So the answer is **\( b. 66.25 \)** meters.

**10th question:**
The quadratic function is \( f(x) = -4.9x^2 + 24.5x + 124 \). Again, you are asked to determine the maximum height of the fireworks.

Using the same process:
- \( a = -4.9 \)
- \( b = 24.5 \)

The \( x \)-coordinate of the vertex is:
\[
x = -\frac{24.5}{2(-4.9)} = 2.5
\]

Now, substitute \( x = 2.5 \) into the function:
\[
f(2.5) = -4.9(2.5)^2 + 24.5(2.5) + 124 = 154.625
\]

So the answer is **\( c. 154.625 \)** feet.

### Answers:
- **9)** \( b. 66.25 \)
- **10)** \( c. 154.625 \)

Would you like more details on how these solutions were derived?

Here are 5 related questions:
1. How do you calculate the axis of symmetry for a quadratic function?
2. What is the formula to find the maximum or minimum point of a quadratic function?
3. How does the sign of the leading coefficient \( a \) affect the shape of a parabola?
4. How can you solve for the roots of a quadratic equation?
5. What are real-life applications of quadratic functions?

**Tip:** For any quadratic function, the vertex formula \( x = -\frac{b}{2a} \) is key to finding the maximum or minimum values of the function.

Discover how to find the maximum height for quadratic functions like f(x) = -5x^2 + 35x + 5 and f(x) = -4.9x^2 + 24.5x + 124 using the vertex formula. Suitable for Grade 9 students learning about parabolas and quadratic equations.

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