We are given the following equation:
[tex]y=2x^2+36x+170[/tex]
To transform this to vertex form we will first take 2 as a common factor:
[tex]y=2(x^2+18x+85)[/tex]
Now we will rewrite the expression inside the parenthesis as:
[tex]y=2(x^2+18x+81+4)[/tex]
Now we assotiate terms:
[tex]y=2((x^2+18x+81)+4)[/tex]
Factoring the expression inside the parenthesis:
[tex]y=2((x+9)^2+4)[/tex]
Using the distributive property:
[tex]y=2(x+9)^2+8[/tex]
And thus we get the equation in vertex form.
