Ok, here you go...
given :- y=(x+a)(x+b)
to find where it intersects x-axis, y co-ordinate should be 0.
Subsititue y=0 in the equation. you get
(x+a)(x+b) = 0 ------> Equation 1
meaning x can be -a or -b.
So the two co-ordinates are (-a,0) and (-b,0).
Now, using other given information -
(1) a + b = -1.
(2)The graph intersects the y-axis at (0,-6)
For this, do the same thing, subsitiute x=0 and y=-6 in the equation,
you get : x^2 + x(a+b) + ab = y
=> ab = -6
Now you have a+b = -1 and ab = -6
Substitute this back into the equation (1) to find out values for x
(x+a)(x+b) = 0
=> x^2 + x(a+b) + ab = 0
=>x^2 -x - 6 = 0
=>(x-3)(x+2) = 0
Hence, the two points where graph intersects are (3,0) and (-2,0)
Problem Solved
Whenever you get such co-ordinate geomtry problems, trying using the given data and subsituting in the equations given.
