Question

How do you graph a quadratic function without plugging in points `y= 2(x-3)^2+4`?

Answer 1

Basically you need:
1] The `y` axis intercept; obtained setting `x=0`
2] The vertex; obtained as:
`x_v=-b/(2a)`
`y_v=-Delta/(4a)=-(b^2-4ac)/(4a)`
When your function is in the form `y=ax^2+bx+c`
3] Possible intercepts on the `x` axis; obtained setting `y=0`.