What is the axis of symmetry and vertex for the graph #y = x^2 – 4x – 12#?

1 Answer
Jul 24, 2016

Axis of symmetry #-> x= +2#

#"Vertex" ->(x,y)=(2,-16)#

Explanation:

#color(blue)("Using a bit of a cheat to find "x_("vertex"))#

Given#" "y=x^2color(magenta)(-4)x-12#.....................Equation (1)

#ul("Axis of symmetry is the x value of the vertex")#

#color(green)(x_("vertex")=(-1/2)xx(color(magenta)(-4)) = +2)#

'.....................................................................................................
#color(brown)("A note about what I have just done:")#
Consider the standard form #y=ax^2+bx+c#

Write as #y=a(x^2+b/ax)+c#

Then #x_("vertex")=(-1/2)xxb/a#

In the case of this question #a=1#
'..................................................................................................

#color(blue)("Determine "y_("vertex"))#

Substitute #x=2# into Equation (1)

#color(brown)(y=x^2-4x-12" "->" "y_("vertex")=(color(blue)(2))^2-4(color(blue)(2))-12#

#color(green)(y_("vertex")=4-8-12 = -16)#

#"VERTEX" ->(x,y)=(2,-16)#