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

##### 1 Answer
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:
$y = a {x}^{2} + b x + c$
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:
${x}_{v} = - \frac{b}{2 a} \mathmr{and} {y}_{v} = - \frac{\Delta}{4 a}$;
(Where $\Delta = {b}^{2} - 4 a c$);
2) Y-axis intecept: The coordinates of this pont are given as: $\left(c , 0\right)$;
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:
$a {x}^{2} + b x + c = 0$

In your case you have:

With only these points we can already plot our parabola: