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

1 Answer
TreeReader
Aug 19, 2017

Axis of symmetry: x=-0.5
Vertex: (-0.5,9.75)

Explanation:

Factorising to find roots:
#-(x^2+x-9)# (I took out the -1 because I find it easier to factorise without that extra negative in there confusing things)
#-(x+5)(x-4)#
#x=-5, x=4#

Half way between these points is the axis of symmetry and the vertex.
Total distance between the points: 9
Half that: 4.5
So the axis of symmetry is at #x=(-5+4.5)= -0.5#

Now we also know the x value of the vertex: -0.5. Substituting this back into the original equation will give the y value:
#-(-0.5)^2-(-0.5)+9=y#
#0.5^2+0.5+9=y#
#0.25+0.5+9=y#
#y=9.75#

Therefore vertex at #(-1/2, 9.75)#

graph{-x^2-x+9 [-7, 7, -15, 10]}

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