The function d=0.006s squared represents the braking distances d in meters of a car at a speed s in kilometer per second.Graph the funtion.

The function d=0.006s² represents the braking distances d in meters of a car at a speed s in kilometer per second.Graph the function. Then use your graph to estimate the speed of the car if its braking distance is 12 meters

Part 1) Graph the function

Let

s ----> the speed in kilometers per second

d ----> the braking distances in meters

we have

[tex]d=0.006s^2[/tex]

This is a quadratic equation (vertical parabola) open upward (the leading coefficient is positive)

The vertex represent a minimum

The vertex is the origin

The axis of symmetry is the y-axis

Find the values of d for different values of s

so

For s=0 km/sec ----> [tex]d=0.006(0)^2=0\ m[/tex] ---> point (0,0)

For s=20 km/sec ----> [tex]d=0.006(20)^2=2.4\ m[/tex] ---> point (20,2.4)

For s=30 km/sec ----> [tex]d=0.006(30)^2=5.4\ m[/tex] ---> point (30,5.4)

For s=40 km/sec ----> [tex]d=0.006(40)^2=9.6\ m[/tex] ---> point (40,9.6)

For s=50 km/sec ----> [tex]d=0.006(50)^2=15\ m[/tex] ---> point (50,15)

To graph the function plot the points and connect them

see the attached figure

Part 2) Use your graph to estimate the speed of the car if its braking distance is 12 meters

Looking at the graph

For d=12 m

The value of s is approximately 45 km/sec

see the attached figure