Answer: Is -4x a slope? Graph x^2-4x+3

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In summary, the given equation y=x^2-4x+3 can be graphed as a parabola with a vertex of (2, -1) opening upward. The slope of the line is not -4x and cannot be calculated without using a tangent line. The suggested methods for graphing without using a calculator include completing the square and creating a list of x-y values. It is important to understand the shape of the graph, which is a parabola, in order to accurately graph the equation.
  • #1
ocean09
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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!
 
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  • #2
Do you know what kind of shape the graph has?
 
  • #3
Yes, a parabola.
 
  • #4
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
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
HallsofIvy said:
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.


How would you graph this equation w/out plugging in points or using a calculator?
 
  • #7
ocean09 said:
How would you graph this equation w/out plugging in points or using a calculator?

Why would you want to graph it?
 
  • #8
b/c i want to know how to graph it :smile:
 
  • #9
ocean09 said:
b/c i want to know how to graph it :smile:

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
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
HallsofIvy said:
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.

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:

1. What is the equation for "Graph x^2-4x+3"?

The equation for "Graph x^2-4x+3" is y = x^2-4x+3.

2. What is the shape of the graph of x^2-4x+3?

The shape of the graph of x^2-4x+3 is a parabola.

3. What are the x-intercepts of the graph of x^2-4x+3?

To find the x-intercepts, set y=0 and solve for x. In this case, x^2-4x+3=0 can be factored into (x-3)(x-1)=0. Therefore, the x-intercepts are x=3 and x=1.

4. What are the y-intercepts of the graph of x^2-4x+3?

To find the y-intercept, set x=0. In this case, y = 0^2-4(0)+3 = 3. Therefore, the y-intercept is y=3.

5. What is the vertex of the graph of x^2-4x+3?

The vertex of the graph of x^2-4x+3 can be found using the formula x = -b/2a and y = f(x), where a is the coefficient of x^2, b is the coefficient of x, and f(x) is the equation. In this case, x = -(-4)/2(1) = 2 and y = 2^2-4(2)+3 = -1. Therefore, the vertex is (2,-1).

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