Question 1192078
<font color=black size=3>
y = 2x^2-10x-1
It is of the form y = ax^2+bx+c
a = 2
b = -10
c = -1


The value of h is
h = -b/(2a)
h = -(-10)/(2*2)
h = 10/4
h = 5/2
h = 2.5


Plug this into the original equation
y = 2x^2 - 10x - 1
y = 2(2.5)^2 - 10(2.5) - 1
y = -13.5


The vertex is located at (h,k) = (2.5, -13.5)
The vertex form equation is y = 2(x-2.5)^2 - 13.5
As the name implies, the vertex form equation allows us to quickly determine the vertex.


The graph is below. I used GeoGebra to make the graph.
Desmos is another free tool you can use.
<img src = "https://i.imgur.com/r8XUEGE.png">
Each (x,y) point on the parabola above can be organized to form this table of values<table border = "1" cellpadding = "5"><tr><td>x</td><td>y</td></tr><tr><td>-1</td><td>11</td></tr><tr><td>0</td><td>-1</td></tr><tr><td>1</td><td>-9</td></tr><tr><td>2</td><td>-13</td></tr><tr><td><font color=red>2.5</font></td><td><font color=red>-13.5</font></td></tr><tr><td>3</td><td>-13</td></tr><tr><td>4</td><td>-9</td></tr><tr><td>5</td><td>-1</td></tr><tr><td>6</td><td>11</td></tr></table>where the row highlighted in red is the vertex (2.5, -13.5)
To form such a table, plug in the x values listed to get paired y values. 
Feel free to include other x values as well. Plot as many points as you need.
</font>