## Question

###### What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola #f(x)=x^2 -2x -15#?

What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola #f(x)=x^2 -2x -15#?

## Answers

You can factorise:

#=(x+3)(x-5)# ## Explanation:

This gives you the

zero-points#x=-3andx=5#

Halfway between these lies theaxis of symmetry:

#x=(-3+5)//2->x=+1#

The vertex is on this axis, so putting in#x=1# :

#f(1)=1^2-2.1-15=-16#

So thevertex#=(1,-16)#

Since the coefficient of#x^2# is positive, this is aminumum

There is no maximum, so therangeis#-16<=f(x)< oo#

Since there are no roots or fractions involved the domain of#x# is unlimited.

graph{x^2-2x-15 [-41.1, 41.1, -20.55, 20.52]}

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