Question

What is the vertex form of `y=1/5x^2+7/13x-2`?

Answer 1

`y = (1/5)(x + 35/36)^2 - 1597/676`

Explanation:

`y = (x^2)/5 + (7x)/13 - 2`
x-coordinate of vertex:
`x = -b/(2a) = ((-7)/13)(5/2) = - 35/26`
y-coordinate of vertex:
`y(-35/26) = (1/5)(1225)/676) - (7/13)(35/26) - 2 =`
= 245/676 - 245/338 - 2 = - 245/676 - 1352/676 =
= - 1597/676
Factored form of y:
`y = a(x + b/(2a))^2 + y(-b/(2a))`
`y = (1/5)(x + 35/26)^2 - 1597/676`