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

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May 21, 2018

Answer:

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.

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