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

May 21, 2018

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

Explanation:

$a {x}^{2} + b x + c$

$y = 2 {x}^{2} + 0 x + 6$

a=2
b=0
c=6

y-intercept: $y = c = 6$

axis of symmetry: $a o s = \frac{- b}{2 a} = \frac{- 0}{2 \cdot 2} = 0$

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 $\pm i \sqrt{3}$.

whether it has a maximum $\left(a > 0\right)$ or minimum $\left(a > 0\right)$, yours has a minimum at 6.