Write the quadratic equation y = x^2 - 6x + 7 in vertex form

vertex form :  y  = ( x  - 3)^2   - 2

Step-by-step explanation:

y = x^2 - 6x + 7 in vertex form

we will need to complete the square

so  focus on   x^2  - 6x   only

take -6     divide it by 2  and square it  to get 9

x^2  - 6x   + 9    - 9

so...

y =  x^2  - 6x  + 9    - 9  + 7

y  = ( x  - 3)^2   - 9 + 7

y  = ( x  - 3)^2   - 2

vertex form :  y  = ( x  - 3)^2   - 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.