Question

The quadratic function:
`y=-x^2-8x+1` has an axis of symmetry of
`x=-4`. Which of the following represents the range of the function?

1) [17, ♾️)
2) (-♾️,17]
3) (-♾️,-4]
4) [-4,♾️)

Answer 1

2) (-∞, 17]

Explanation:

The leading coefficient of the function is negative, so the parabola opens downward. The vertex will be a maximum, the upper end of the range. The lower end of the range will be -∞.

The vertex of the function lies on the axis of symmetry. The maximum can be found by evaluating the function at x=-4.

y = -(-4)² -8(-4) +1 = -16 +32 +1 = 17

The range of the function is (-∞, 17].