The table below shows the height of a ball x seconds after being kicked. A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2, 2.5, 3. The second column is labeled height (feet) with entries 0, 35, 65, 85, 95, 100, 95. What values, rounded to the nearest whole number, complete the quadratic regression equation that models the data? f(x) = x2 + x + 0 Based on the regression equation and rounded to the nearest whole number, what is the estimated height after 0.25 seconds? feet

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.

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