What is the axis of symmetry and vertex for the graph #y=3x^2-9#?

1 Answer
Tony B
Apr 16, 2016

Axis of symmetry #->x=0#

Vertex# ->(x,y)->(-9,0)#

Explanation:

Consider the standard form of #y=ax^2+bx+c#

Given:#" "y=3x^2-9#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("General shape of the graph")#

The three in front of #x^2# is positive so the graph is of general shape #uu#. Suppose it was -3. Then the general shape for that scenario would be #nn#

So the shape of #uu# means we have a minimum.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Axis of symmetry")#

There is no term for the equation part #bx# thus the graphs axis of symmetry is #x=0#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Vertex")#

Suppose you just had #color(brown)(y=3x^2)# then the minimum would be at #color(brown)(y=0)#

However, we have #color(brown)(y=3x^2)color(blue)( -9)# so the vertex lowers by 9.

#color(green)(y_("vertex")->color(brown)(y=0color(blue)(-9))=-9)#

Tony B

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