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

Question

1571 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-05T09:52:20

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

$Y=x^2−4x+5$

It is a quadratic equation.
Find the vertex
$x=(-b)/(2a)=(-(-4))/(2 xx1)=4/2=2$
At $x=2 : y = (2^2)-4(2)+5$
$y = 4-8+5=9-8=1$

Its vertex is $(2, 1)$
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

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