SOLUTION: For the quadratic function​ defined, ​(a) write the function in the form P(x)=a(x-h)^2+k​, ​(b) give the vertex of the​ parabola, and ​(c) graph the function. ​P(x)=

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Question 1192078: For the quadratic function​ defined, ​(a) write the function in the form P(x)=a(x-h)^2+k​, ​(b) give the vertex of the​ parabola, and ​(c) graph the function.
​P(x)=2x^2-10x-1
any help would be great thank you so much!
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

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.

Each (x,y) point on the parabola above can be organized to form this table of values
xy
-111
0-1
1-9
2-13
2.5-13.5
3-13
4-9
5-1
611
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.
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