How do you find the axis of symmetry, and the maximum or minimum value of the function #f(x) = -3x^2 - 6x - 2#?

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Answer 1 · 2018-03-22T01:33:39

Axis of symmetry: #x=-1#

Vertex: #(-1,1)#

#f(x)=-3x^2-6x-2# is a quadratic equation in standard form:

#ax^2+bx+c#,

where:

#a=-3#, #b=-6#, #c=-2#

Axis of symmetry: vertical line that divides a parabola into two equal halves

The formula for finding the axis of symmetry for a quadratic equation in standard form is:

#x=(-b)/(2a)#

#x=(-(-6))/(2*-3)#

Simplify.

#x=6/(-6)#

#x=-1#

The axis of symmetry is #x=-1#.

Vertex: minimum or maximum point of a parabola

Since #a<0#, the vertex is the maximum point and the parabola will open downward.

The #x#-value of the vertex is the axis of symmetry.

To find the #y#-value, substitute #-1# for #x#, and substitute #f(x)# for #y#.

#y=-3(-1)^2-6(-1)-2#

Simplify.

#y=-3+6-2#

#y=1#

The vertex is #(-1,1)#.

graph{y=-3x^2-6x-2 [-10, 10, -5, 5]}