Graphing question

[awilhelm]

Please help with the following question:

In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

1) a + b = -1
2) The graph intersects the y-axis at (0, -6)

Thanks!

[tritrantran]

Please help with the following question:

In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

1) a + b = -1
2) The graph intersects the y-axis at (0, -6)

Thanks!

So when it intersects the x-axis, y = 0.

0 = (x+a)(x+b)
x = -a or x = -b

Statement (1)
a + b = -1
A and B could be multiple values....INSUFFICIENT

Statement (2)
The graph intersects the y-axis at (0, -6)
y = (x + a)(x + b)

-6 = (0+a)(0+b)
-6 = ab
A and B could be multiple values...INSUFFICIENT

St (1) and St (2)
a + b = -1
-6 = ab

-6 = (-1 - b)*b
-6 = -b - b^2
b^2+b-6 = 0

b= -3 or b = 2

If b = -3, then a = 2
If b = 2, then a = -3

y = (x+2)(x-3) or
y= (x-3)(x+2)


SUFFICIENT (C)

[awilhelm]

Thanks a lot!

[awilhelm]

Near the end of your reply, you say:

b= -3 or b = 2

If b = -3, then a = 2
If b = -2, then a = 1 ( doesn't work -6 = ab)
So a = 2, b =-3

But why are you offering -2 as a possible value for b? The equations are:
-6 = ab
a + b = -1

So if b = -3, then a = 2
but if b = 2, then a = -3

We don't know which values for a and b are correct, no??

[tritrantran]

Near the end of your reply, you say:

b= -3 or b = 2

If b = -3, then a = 2
If b = -2, then a = 1 ( doesn't work -6 = ab)
So a = 2, b =-3

But why are you offering -2 as a possible value for b? The equations are:
-6 = ab
a + b = -1

So if b = -3, then a = 2
but if b = 2, then a = -3

We don't know which values for a and b are correct, no??

My mistake...

So if b = -3, a = 2
or b =2, a = -3

y = (x+2)(x-3) or
y = (x-3)(x+2)

This is still the same equation (C)

[awilhelm]

Got it, thanks again!

[ronniecoleman]

IMO C