Question

In a polynomial function, is the constant always the y intercept?

For example:

f(x) = x^3 - 33x^2 +216x - 2

Is the y intercept at y=-2?

Answer 1

I'd say no, because graphing that function gives the y intercept to be at y=0

Answer 2

Can you explain further how you got that the y intercept is 0?

Answer 3

Input x = 0?

Answer 4

Not quite. Replace the f(x) in the function with y.
y = x^3 - 33x^2 +216x - 2
Then enter that into your graphing calc

Answer 5

The y-intercept is where the graph crosses the y-axis, which means \(x=0\).

Notice what happens to every variable term as \(x=0\), and how the constant is not affected.

Answer 6

Yeah so to find the y intercept you simply do f(0)?

Answer 7

Yes.

The actual graph of the function is incredibly steep at x=0, so the graph is kind of hard to read there. It isn't at y=0 though.

Answer 8

True, @AccessDenied , had used an unsuitable scale.

Answer 9

allank I think your mistake was that you looked at a graph on a calculator rather than solving for the y intercept

Answer 10

@ConfusedAboutCalculus Graphing does work, though

Answer 11

Didn't work for you this time :P

Answer 12

Heheh, didn't use a good scale, and saw the graph as if crossing the y axis at zero. Gimme a break :)

Answer 13

Yeah, the slope around x=0 is in the hundreds for rise/run (285/1 at x=-1, 216/1 at x=0, 153/1 at x=1...). :P

Answer 14

;)