How do you graph y=x^2-2x+3?

1 Answer
Gió
Dec 29, 2014

You can look at the "special" points of your function. These are points that characterize the curve represented by your function.
In your case you have a quadratic in the general form given as:
y=ax^2+bx+c
which is represented, graphically, by a PARABOLA. The orientation of the parabola is given by the coefficient a of x^2; in this case you have a=1>0 so this is an upward parabola, i.e. like a U.

Now the special points:
1) You find the VERTEX (the lowest point of your parabola) which has coordinates given by:
x_v=-b/(2a) and y_v=-Delta/(4a);
(Where Delta=b^2-4ac);
2) Y-axis intecept: The coordinates of this pont are given as: (c,0);
3) X-axis intercept(s): the coordinate of these intercepts (if they exist) are given by putting y=0 and solving the second degree equation:
ax^2+bx+c=0

In your case you have:
enter image source here
With only these points we can already plot our parabola:
enter image source here

Related questions
See all questions in Quadratic Functions and Their Graphs
Impact of this question
42580 views around the world
You can reuse this answer
Creative Commons License