Question

What are the important points needed to graph `y=2x^2+6`?

Answer 1

y-intercept
axis of symmetry
vertex
x-intercept(s) if it has any real ones
whether it has a maximum or minimum

Explanation:

`ax^2+bx+c`

`y=2x^2+0x+6`

a=2
b=0
c=6

y-intercept: `y= c = 6`

axis of symmetry: `aos=(-b)/(2a) = (-0)/(2*2) = 0`

vertex = #(aos, f(aos)) = (0, 6)

x-intercept(s) if it has any real ones, these are the solutions or roots when you factor you polynomial. Yours has only imaginary roots `+-isqrt3`.

whether it has a maximum `(a>0)` or minimum `(a>0)`, yours has a minimum at 6.