We are given that y = x^2 + 5x + 6
We can see that the equation given is already in a standar form of y = ax^2+bx+c
What to note also is that the co-eficient a is positive, so we expect a smiley graph
We also take note that our c in this case is 6, this represent the y intercept = 6
Now lets find the x- intercepts:
We do this by factorising our equation as follows when y =0 :
(x +3 ) (x +2 ) =0
So this means (x+3) =0; therefore x = -3
Similarly (x+2) =0; therefore X = -2
We need to also determine, what is Y when x = -3 and when x= -2 respectively , by replacing it back into the original equation
therefore Y = (-3)^2 + 5(-3) +6 = 9 -15+6 = 0
similary, Y = (-2)^2 + 5(-2) +6 = 4 -10 +6 + 0
This can be represented as ( -3,0) and (-2, 0) with y intercept of ( 0;6)