Question

How do you identify the important parts of `y= x^2 - 4x` to graph it?

Answer 1

Vertex `(2,-4)`

Axis of symmetry `x=2`
since the co-efficient of `x^2` is positive, the curve is concave upwards. It has a minimum.

Explanation:

Given -
`y=x^2-4x`
It is a quadratic function of the form `y = x^2+bx+c`
In the given function the constant term is absent.
So we shall have it as '0'.
`y=x^2-4x+0`
The presence or absence of constant term is not going to affect our answer.

Find the vertex
`x=(-b)/(2a)=(-(-4))/(2 xx 1)=4/2=2`
`y=2^2-4(2)=4-8=-4`

Vertex `(2,-4)`

Axis of symmetry `x=2`
since the co-efficient of `x^2` is positive, the curve is concave upwards. It has a minimum.