How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=-2x^2+6#?

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Answer 1 · 2016-03-26T20:59:04

Axis of symmetry at #x=0#

Maximum #->(x,y)->(0,6)#

Given:#" "y=-2x^2+6#

The coefficient of #x^2# is negative so the generic shape of the graph is #nn#. Thus we have a maximum.

The maximum will occur at the axis of symmetry which is also #x_("vertex")#

As there is no #bx# term from #y=ax^2+bx+c# then the axis of symmetry is at #x=0#

Otherwise it would be at #x=(b/a)xx(-1/2)# In fact it is as

#x=(0/(-2))xx(-1/2)=0#

#color(blue)(y_("vertex")=-2(0)+6 = 6#

#color(blue)("So maximum "->(x,y)->(0,6)#