# Graph x^2-4x+3

1. Sep 3, 2006

### ocean09

Graph x^2-4x+3.

My question:

1) is -4x a slope?

I'm trying to graph this equation w/out using a calculator or plugging in points.

Thanks!

2. Sep 3, 2006

### Hurkyl

Staff Emeritus
Do you know what kind of shape the graph has?

3. Sep 3, 2006

### ocean09

Yes, a parabola.

4. Sep 3, 2006

### shmoe

You might try completing the square, this should make it clear how it relates to the graph of the good old y=x^2.

5. Sep 3, 2006

### HallsofIvy

No, "-4x" is not a slope. The slope of a line is a number. If y= mx+ b then the slope is the number m. In the example given, y=x2- 4x+ 3, the graph is not a line and so doesn't have a slope. One definition of "derivative" is that the derivative, at any given value of x, is the slope of the tangent line.

6. Sep 3, 2006

### ocean09

How would you graph this equation w/out plugging in points or using a calculator?

7. Sep 3, 2006

### CRGreathouse

Why would you want to graph it?

8. Sep 3, 2006

### ocean09

b/c i want to know how to graph it

9. Sep 3, 2006

### d_leet

You know that it looks like a parabola. Are you familiar with the vertex form of the equation for a parabola? If so then doing what shmoe suggested would help you graph it.

10. Sep 4, 2006

### HallsofIvy

Well, I think it was in fifth grade where they taught me to make a list of x y values:

x y= x2- 4x+ 3
0 3
1 1- 4+ 3= 0
-1 1+ 4+ 3= 8
2 4- 8+ 3= -1
-2 4+ 8+ 3= 15
3 9- 12+ 3= 0
-3 9+ 12+3= 24
etc, mark the points (0,3), (1, 0), (-1, 8), (2, -1), (-2, 15), (3, 0), (-3, 24) and then draw a smooth curve through the points.

Another method, that I think I didn't learn until 9th or 10th grade was to complete the square: if y= x2- 4x+ 3= x2- 4x+ 4- 4+ 3= (x- 2)2- 1. The graph is a parabola with vertex (2, -1) opening upward.

11. Sep 4, 2006

### ocean09

i was looking through my math book, and it showed me how to graph it.

it doesn't hurt to sound stupid sometimes. at least, you are learning something.

Last edited: Sep 4, 2006