Question

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

Answer 1

Its vertex is `(2, 9)`
Axis of symmetry `x=2`
The co-efficient of `x^2` is positive, the curve is concave upwards.
It has a minimum. graph

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=4-13=9`

Its vertex is `(2, 9)`
Axis of symmetry `x=2`
The co-efficient of `x^2` is positive, the curve is concave upwards.
It has a minimum.
Take three points on either side of `x=2` and find the y values.
plot all the points. Join them with a smooth line

x: y
-1: 0
0: -5
1: -8
2; -9
3: -8
4: :-5
5; 0

graph{x^2-4x-5 [-22.8, 22.83, -11.4, 11.4]}