Sketching Polynomial Functions

[myusername]

I'm trying to sketch polynomial functions, and there are a few things I don't understand (I've included pictures).

1. The first polynomial I had to graph was y= (x-2)(x+3)
According to my textbook, the answer is:

I understand 2 and -3 being the x-intercepts, but is there any particular reason why the factor crosses the y axis at the point that it does?

2. I had to sketch y=x(x-1)(x-3) and it looks like this, according to my textbook:

Again, is there any significance to the point where the sketch crosses the y axis? And what about the exact curve between the two points on the graph? Would my sketch still be right if they curved a little more/less?

3. According to my textbook, when you sketch -x^2(x-3)(x+2) you end up with this:

We learned this thing where if the exponent is even it will "kiss" (curve away from?) the x-axis, and if it is odd it will cross the x-axis. What does this mean? How do I know if my exponent is odd or even? If we have to "kiss" or curve away from the x-axis, by how much do we have to do this?

Please can someone help me? I have a test soon and I'm really confused.

 

[royhaas]

The curves cross the y axis whenever x=0. Your last graph is not consistent with the equation you wrote.

 

[Deleted member 4993]

I'm trying to sketch polynomial functions, and there are a few things I don't understand (I've included pictures).

1. The first polynomial I had to graph was y= (x-2)(x+3)
According to my textbook, the answer is:

I understand 2 and -3 being the x-intercepts, but is there any particular reason why the factor crosses the y axis

Yes - very important - that is y-intercept. It is the value of the function when x = 0. In this case, y = -6 when x=0


at the point that it does?

2. I had to sketch y=x(x-1)(x-3) and it looks like this, according to my textbook:

Again, is there any significance to the point where the sketch crosses the y axis?

Yes - very important - that is y-intercept. It is the value of the function when x = 0. In this case, y = 0 when x=0
And what about the exact curve between the two points on the graph? Would my sketch still be right if they curved a little more/less? - Not very important

3. According to my textbook, when you sketch -x^2(x-3)(x+2) you end up with this:

We learned this thing where if the exponent is even it will "kiss" (curve away from?) the x-axis, and if it is odd it will cross the x-axis. What does this mean? How do I know if my exponent is odd or even(odd or even number i.e. 3 is odd & 4 is even)? If we have to "kiss" or curve away from the x-axis, by how much do we have to do this?

Please can someone help me? I have a test soon and I'm really confused.