Answer:
The vertex form of the equation is [tex]y=2(x-3)^2+7[/tex]
Step-by-step explanation:
Given equation in standard form:
[tex]y=2x^2-12x+25[/tex]
Completing square method:
Equating the given function to [tex]0[/tex].
[tex]2x^2-12x+25=0[/tex]
Subtracting both sides by [tex]25[/tex].
[tex]2x^2-12x+25-25=0-25[/tex]
[tex]2x^2-12x=-25[/tex]
Taking common factor [tex]2x[/tex].
[tex]2(x^2-6x)=-25[/tex]
Dividing [tex]-6[/tex] by [tex]2[/tex] then adding and subtracting the square of it from the whole term in parenthesis
[tex]2(x-6x+(\frac{6}{2})^2-(\frac{6}{2})^2)=-25[/tex]
[tex]2(x^2-6x+9-9)=0[/tex]
[tex][x^2-6x+9][/tex] can be written as [tex](x-3)^2[/tex].
[tex]2((x-3)^2-9)=-25[/tex]
Using distribution.
[tex]2(x-3)^2-18=-25[/tex]
Adding both sides by 25.
[tex]2(x-3)^2-18+25=-25+25[/tex]
[tex]2(x-3)^2+7=0[/tex]
Equating the above function with [tex]y[/tex]
[tex]y=2(x-3)^2+7[/tex]
∴ The vertex form of the equation is [tex]y=2(x-3)^2+7[/tex]
