Question

What is the vertex form of `y=7x^2 +3x + 5`?

Answer 1

`y = 7(x + 3/14)^2 + 917/196`

Explanation:

The vertex form of a quadratic equation `y=ax^2 +bx +c` is `y=a(x+m)^2 +n`, where `m = b/(2a)` and `n = -a(b/(2a))^2 + c`
Then the vertex is at the point where the bracketed expression is zero and is therefore `(-m,n)`
Therefore `y = 7(x+3/14)^2 -7*9/196 +5`
`y = 7(x +3/14)^2 - (63 + 980)/196`
`y = 7(x + 3/14)^2 + 917/196`