What is the axis of symmetry and vertex for the graph #y=-2x^2+4x+3#?

1 Answer
Tony B
Feb 25, 2016

Axis of symmetry#" "->x-1#
#color(white)(.)#
Vertex#" "->(x,y)->(1,5)#

Explanation:

First consider the #-2x#. As this is negative the general shape of the graph is #nn#

The axis of symmetry will be parallel to the y-axis (normal to the x-axis) and pass through the vertex
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This next bit is a variant on the vertex form equation

Given:#" "y=-2x^2+4x+3" "#........................................(1)

Write as:#" "y=-2(x^2-4/2x)+3#

Consider the #-4/2 " from "-4/2x#

Apply this process:#" "(-1/2)xx(-4/2)=+1#

This value of #+1# is the value of #x_("vertex")#

#color(brown)("So "x=1 " is the axis if symmetry.")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute #x=1# into equation (1) to find#" "y_("vertex")#

#=>y=-2(1)^2 +4(1)+3 = 5#

#color(brown)("Vertex" ->(x,y)->(1,5))#

Tony B

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