Dylan is riding his motorcycle from his house to his friend's house 125 miles away. The graph to the right shows the distance he is away from his house
based on the time he has travelled.
1
After riding for 4 hours how far is Dylan from his house?
2
How many hours did it take Dylan to ride 75 miles?
3.
What might Dylan be doing between hour 2 and 3?
4. Is Dylan travelling faster during the first hour (between hour
O and 1) or the 2nd hour (between hour 1 and 2)?

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.