Serious Math Question! Is my LOGIC correct? ?

Question

i just created this problem out of my head

f(x) = 3x^2 + 4x + 6

i want to find the y-intercepts

so does that mean that i have to set x to zero?

f(0) = 3(0)^2 +4(0)+6

f(0) = 6

the y-intercept is 6? (0,6)

the reason i think this is true is because i read in my textbook that the y-intercept is (0,b) where the input or domain is 0 and the output is the y-intercept

is (0, b)

Answer 1

Yes, your logic is correct.  This is because the Y axis is - by definition - the line: x = 0.

To answer your second question: Because your equation is a trinomial, there is only 1 point at which the shape that you graph (a parabola) crosses the Y axis.  However, if it were a circle (4 = √x² + y²) then you there would be two places that it crosses, so you would need to make sure and find both of them.

Answer 2

As long as y = f(x), your logic is correct.

Answer 3

It's correct.Y intercept> x = 0. I think it's working on other functions also. Why don't you have a try then?

^_^

Answer 4

yes you're right  

Answer 5

Yes.  The Y intercept is the point(s) at which a curve passes through the Y axis.  By definition that means X = 0, but remember that there may be more than one Y intercept.  For example, the parabola you used opens upwards.  What about one that opened left or right (ie:  x = 3y^2 + 4y + 6)  That would have 2 Y intercepts.  Similarly, a cubic could have 3 intercepts, etc.

Answer 6

yeeah your right