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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-> 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):
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
x
y
-1
11
0
-1
1
-9
2
-13
2.5
-13.5
3
-13
4
-9
5
-1
6
11
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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