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

1 Answer
Nallasivam V
Oct 5, 2015

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.

Explanation:

#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

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