Question

How do you express `y=5x^2-3x+2` in vertex form?

Answer 1

`y = 5(x-3/10)^2+31/20`

Explanation:

`y=5x^2-3x+2`

`=5(x^2-3/5x+2/5)`

`=5(x^2-3/5x+9/100-9/100+2/5)`

`=5(x-3/10)^2+5(2/5-9/100)`

`=5(x-3/10)^2+(40-9)/20`

`=5(x-3/10)^2+31/20`

Bringing the two ends together, we have:

`y = 5(x-3/10)^2+31/20`

which is in vertex form:

`y = a(x-h)^2+k`

with vertex `(h, k) = (3/10, 31/20)` and multiplier `a=5`