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

Answer 1

You can factorise: #=(x+3)(x-5)#

This gives you the zero-points #x=-3andx=5# Halfway between these lies the axis 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 the vertex #=(1,-16)# Since the coefficient of #x^2# is positive, this is a minumum There is no maximum, so the range is #-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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Answer 2

Vertex: (1, -16/4) or (1, -4)

Axis of symmetry: x = 1

Maximum/Minimum value: The parabola opens upwards, so it has a minimum value. The minimum value occurs at the vertex.

Range: Since the parabola opens upwards, the range is all real numbers greater than or equal to the minimum value. So, the range is [-16/4, ∞) or [-4, ∞).

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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.

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.

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.

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.

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