H(x)=1/2(x+3)^2 + 2 how is the graph of h(x) translated from the parent graph of a quadratic function, f(x)=x^2

The graph is translated 3 to the left and 2 up. When adding a number to x inside the parentheses the graph is moved to the left. When adding to x outside the parentheses the graph will move up. The graph is also strerched by 1/2.

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.