SOLUTION: Please help me solve the following: For the graph of the function f(x)=2x^2-12x+20 Find the vertex; state whether this is a maximum or minimum value and find the value; and f

Question 162833: Please help me solve the following:
For the graph of the function f(x)=2x^2-12x+20
Find the vertex; state whether this is a maximum or minimum value and find the value; and find the range.
I have no idea where to begin to solve this. Any assistance you can provide is greatly appreciated!

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
This site gives some insight into parabolas:
http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php
.
Standard vertex form is:
y= a(x-h)^2+k
where
(h,k) is the vertex
Minimum or maximum is determined by the 'a'.
If a is POSITIVE (think happy face -- smile -- U) -- opens upwards -- will be a minimum.
If a is NEGATIVE (think sad face -- upside down U) -- opens downwards -- will be a maximum.
.
Idea is to get your equation into that form.
f(x)=2x^2-12x+20
Group terms:
f(x)=(2x^2-12x)+20
Factor:
f(x)=2(x^2-6x)+20
Complete the square:
f(x)=2(x^2-6x+9)+20-18
f(x)=2(x-3)^2+2
.
Vertex is then (3,2)
Since 'a' is POSITIVE, it is a MINIMUM.

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