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
Algebra ->
Rational-functions
-> 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
Log On
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!
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.
