Question

Quadratic function has a line of symmetry at x = –3.5 and a zero at –9.

what is the distance from the given zero to the line of symmetry
5.5
what is the other zero of the quadratic function?
2

Answer 1

Explanation:

We need to find the distance from x=-3.5 and ( -9,0).

We can't find a distance from a point to the line using distance formula so we need another approach. Let construct a line perpendicular to the line x=-3.5

That line will be a zero slope because the slope of the orginal line x=-3.5 has a slope undefined. So our equation of the line will be y=0. Now we need to find the point where y=0 and x=-3.5 intersect. That point will be at (-3,5,0). Now we can find distance from (-3.5,0) to (-9,0).

Since the y value is the same, we can just subtract,

`- 9 - ( - 3.5)`

which gives us

`- 5.5`

Rember distance is positive so

`5.5`

is the distance.

The line of symmetry reflects the zero about x=-3.5. So the distance to the other zero is just 5.5 more than -3.5 which is

`- 3.5 + 5.5 = 2`