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!
You might try completing the square, this should make it clear how it relates to the graph of the good old y=x^2.
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=x^{2}- 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.
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.
Well, I think it was in fifth grade where they taught me to make a list of x y values: x y= x^{2}- 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= x^{2}- 4x+ 3= x^{2}- 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.