What is the axis of symmetry and vertex for the graph #y = -2x^2 - 12x - 7#?

1 Answer
Meave60
Aug 9, 2017

The axis of symmetry is #-3# and the vertex is #(-3,11)#.

Explanation:

#y=-2x^2-12x-7# is a quadratic equation in standard form: #ax^2+bx+c#, where #a=-2#, #b=-12#, and #c=-7#.

The vertex form is: #a(x-h)^2+k#, where the axis of symmetry (x-axis) is #h#, and the vertex is #(h,k)#.

To determine the axis of symmetry and vertex from the standard form: #h=(-b)/(2a),# and #k=f(h)#, where the value for #h# is substituted for #x# in the standard equation.

Axis of Symmetry

#h=(-(-12))/(2(-2))#

#h=12/(-4)=-3#

Vertex

#k=f(-3)#

Substitute #k# for #y#.

#k=-2(-3)^2-12(-3)-7#

#k=-18+36-7#

#k=11#

The axis of symmetry is #-3# and the vertex is #(-3,11)#.

graph{y=-2x^2-12x-7 [-17, 15.03, -2.46, 13.56]}

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