Interpreting Algebraic Models Question 7

calculator allowed The gas mileage $M(s)$ , in miles per gallon, of a car traveling $s$ miles per hour is modeled by the function below, where $10 \leq s \leq 100$ .

M(s)= -\frac{1}{20}s^2+6s-25

According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

25

55

60

100

Approach

The question is asking for the speed $s$ where $M(s)$ is the greatest. How would we approach this for a similar quadratic equation?

Gas mileage model

M(s)= -\frac{1}{20}s^2+6s-25

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

Standard quadratic model

y=-ax^2+bx+c

x=-\frac{b}{2a}

The maximum must occur at the vertex of a downward facing parabola!

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

s=-\frac{6}{2\left(-\frac{1}{20}\right)}

s=\boxed{60}