Given that the efficiency $E$ is a quadratic function of speed $s$, we can express this as:

$E(s) = as^2 + bs + c$

We are given three points corresponding to the speed and efficiency values:

• $(12, 0.18)$
• $(22, 0.23)$
• $(30, 0.18)$

These points give us three equations based on the general quadratic formula:

1. $0.18 = a(12)^2 + b(12) + c$
2. $0.23 = a(22)^2 + b(22) + c$
3. $0.18 = a(30)^2 + b(30) + c$

We will solve this system of equations to find the values of $a$, $b$, and $c$, then find the speed $s$ that gives the maximum efficiency by determining the vertex of the quadratic function.

Let's proceed with the calculations.The quadratic function representing the efficiency $E(s)$ in terms of speed $s$ is:

$E(s) = -0.000625s^2 + 0.02625s - 0.045$

To find the speed that gives the maximum efficiency, we need to determine the vertex of this quadratic function. The speed at the vertex of a parabola given by $ax^2 + bx + c$ occurs at:

$s = -\frac{b}{2a}$

Let's calculate the speed $s$ that maximizes the efficiency.The speed that gives the maximum efficiency for descending flight is $21$ mph.

Would you like more details on how the quadratic function was derived or have any other questions?

Here are five related questions to explore further:

1. How does a quadratic function model different types of parabolas?
2. What is the significance of the vertex in real-world applications?
3. How do we determine the direction of the parabola's opening?
4. What role do the coefficients $a$, $b$, and $c$ play in the shape of the graph?
5. How can we verify the correctness of the quadratic model using the given data points?

Tip: The vertex formula $s = -\frac{b}{2a}$ is crucial in finding optimal values in quadratic models, such as maximizing or minimizing real-world quantities.