Question

What is y=4x^2-9x+1 in vertex form

Answer 1

`y = 4 \left(x - (9)/(8) \right)^2 - (65)/(16)`

Explanation:

`y = 4x^2 - 9x + 1`

You need to complete the square on the right side.

`y = (4x^2 - 9x) + 1`

`y = 4(x^2 - (9)/(4)x) + 1`

`y = 4 \left( x^2 - (9)/(4)x + \left( (9)/(8) \right)^2 \right) + 1 - 4\left( (9)/(8) \right)^2`

`y = 4 \left(x - (9)/(8) \right)^2 + 1 - 4 \left( (81)/(64) \right)`

`y = 4 \left(x - (9)/(8) \right)^2 + 1 - (81)/(16)`

`y = 4 \left(x - (9)/(8) \right)^2 + (16)/(16) - (81)/(16)`

`y = 4 \left(x - (9)/(8) \right)^2 - (65)/(16)`