Question

The height of an arch is modeled by the equation y=-x^2-6x+16. Which of the following gives the width of the arch at its base?

the y-coordinate of the vertex
double the x-coordinate of the vertex
the y-intercept of the equation
the difference between the zeroes

Answer 1

Explanation:

the answer is the difference between zeros

Answer 2

we have

`y=-x^2-6x+16`

using a graph tool

see the attached figure

The vertex of the quadratic equation is the point
`(-3,25)`

That means that the maximum height of an arch is equal to
`25\ units`

The zeroes of the function are the points
`(-8,0)\ and\ (2,0)`

That means that the width of the arch at its base is equal to difference between the zeroes

`=(2-(-8))=2+8=10\ units`

therefore

the answer is

The width of the arch at its base is equal to the difference between the zeroes