Question

The center of an ice rink is located at (0, 0) on a coordinate system measured in feet. Sandi skates along a path that can be modeled by the equation y = 0.08x2 - 1.6x + 13. David starts at (20, 13) and skates along a path that can be modeled by a quadratic function with a vertex at (10, 5). Which system of equations models the paths of the two skaters? y = 0.08x2-1.6x+13 and y = 0.08(x-10)2+5 y = 0.08x2-1.6x+13 and y = 1.6(x-10)2+5 y = 0.08x2-1.6x+13 and y = 0.8(x-10)2+5 y = 0.08x2-1.6x+13 and y = 5(x-10)2+5

Answer 1

y = 0.08x2-1.6x+13 and y = 0.08(x-10)2+5 is the correct answer :)

Answer 2

Answer : y =
`0.08x^2 - 1.6x + 13` and y=
`0.08 (x- 10)^2 + 5`

Sandi skates along a path that can be modeled by the equation

y =
`0.08x^2 - 1.6x + 13`

David starts at (20, 13) and skates along a path that can be modeled by a quadratic function with a vertex at (10, 5).

Vertex form of quadratic function is

y =
`a(x-h)^2 + k` where (h,k) is the vertex

We plug in (10,5) for h and k

y=
`a(x-10)^2 + 5`

Now plug in (20,13) in the above equation and find out 'a'

13 =
`a(20 - 10)^2 + 5`

13 =
`a(10)^2 + 5`

13 = 100 a + 5

Subtract 5 on both sides

8 = 100a

a = 0.08

When we plug in 0.08 for 'a' then the equation becomes

y=
`0.08 (x- 10)^2 + 5`