What is the axis of symmetry and vertex for the graph #y = -2x^2 - 6x + 1#?

1 Answer
May 20, 2016

Axis of symmetry#" "->x= -3/2#

Vertex#" "->(x,y)->(-3/2,11/2)#

Explanation:

Write as #y=-2(x^2+3x)+1#

Consider the 3 from #+3x#
#color(green)("Axis of symmetry "-> x_("vertex")=(-1/2)xx(3)=-3/2)#
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Substitute #x=-3/2# in the original equation to determine #y_("vertex")#

#color(brown)(y=-2x^2-6x+1)#

#color(blue)(=>" "y_("vertex")=-2(-3/2)^2-6(-3/2)+1)#

#color(blue)(=>" "y_("vertex")=-2(+9/4)-6(-3/2)+1)#

#color(green)(y_("vertex")=11/2)#

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Tony B