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

Oct 5, 2015

Its vertex is $\left(2 , 9\right)$
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

Find the vertex
$x = \frac{- b}{2 a} = \frac{- \left(- 4\right)}{2 \times 1} = \frac{4}{2} = 2$
At $x = 2 : y = \left({2}^{2}\right) - 4 \left(2\right) - 5$

$y = 4 - 8 - 5 = 4 - 13 = 9$

Its vertex is $\left(2 , 9\right)$
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]}