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

1 Answer
Oct 5, 2015

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]}