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

Answer 1

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

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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Answer 2

Eva Adamson

The axis of symmetry is x = -0.5 and the vertex is (-0.5, 9.25).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.