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.