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

The answers to the question are are the equations

y = 0.08x²-1.6x+13

y = 0.08(x-10)²+5

How to solve for the system of equations

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 = $a(x-h)^2+k$

13 = a(x-10)²+5

let x = 20

a(20-10)²+5

13 = 100a + 5

take like terms

13 - 5 = 100a

8 = 100a

divide through by 100

a = 0.08

hence the equation would be

y = 0.08(x-10)²+5

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