# How do you identify the important parts of Y = x^2 - 4x+5  to graph it?

Oct 5, 2015

Its vertex is $\left(2 , 1\right)$
Axis of symmetry $x = 2$
The co-efficient of ${x}^{2}$ is positive, the curve is concave upwards.
It has a minimum.

#### Explanation:

Y=x^2−4x+5

Find the vertex
$x = \frac{- b}{2 a} = \frac{- \left(- 4\right)}{2 \times 1} = \frac{4}{2} = 2$
At $x = 2 : y = \left({2}^{2}\right) - 4 \left(2\right) + 5$
$y = 4 - 8 + 5 = 9 - 8 = 1$

Its vertex is $\left(2 , 1\right)$
Axis of symmetry $x = 2$
The co-efficient of ${x}^{2}$ is positive, the curve is concave upwards.
It has a minimum.

x: y
-1: 10
0: 5
1: 2
2: 1
3: 2
4: 5
5: 10
graph{x^2-4x+5 [-10, 10, -5, 5]} 10