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

1 Answer
Narad T.
Oct 17, 2016

the axis of symmetry is x=-1
and the vertex is (-1,-4)

Explanation:

#y=x^2+2x-3#
Rewrite the equation in the vertex form
#y=x^2+2x+1-4=(x+1)^2-4#
The line of symmetry is when#(x+1=0)#
And the vertex is on that line#(-1,-4)#

If you have not yet studied calculus, forget what I write under

Differentiating with respect to x
#dy/dx=2x+2#
The vertex is when #dy/dx=0#
#2x+2=0=>x=-1# and #y=(-1)^2+(2*-1)-3=1-5=-4#
Differentiating once more
#(d^2y)/dx^2=2 (>0)# so we have a minimum

Here is a graph of the function
graph{x^2+2x-3 [-10, 10, -5, 5]}

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