Question

N the same coordinate system, a motorboat starts at (2, 3) and travels toward the island along a path that can be modeled with a quadratic function with a vertex at (-1,-1.5). (x,y) = the boat's position vertex form of a quadratic equation: y = a(x - h)2 + k what equation models the path of the motorboat in the coordinate system?

Answer 1

y = 0.5(x - (-1)^2 + (-1.5)

Explanation:

Answer 2

`y=0.5(x+1)^(2) -1.5`

Explanation:

We know that,

The equation representing the quadratic function having the vertex ( h,k ) is given by
`y=a(x-h)^(2)+k`.

As, the vertex for the given system is ( -1,-1.5 ). We get the equation is,

`y=a(x+1)^(2)-1.5`.

Now, as the motorboat starts at ( 2,3 ). Substituting the values in above equation gives us,

`3=a(2+1)^(2)-1.5`.

i.e.
`3=a3^(2)-1.5`.

i.e.
`3=9a-1.5`.

i.e.
`9a=3+1.5`.

i.e.
`9a=4.5`.

i.e.
`a=(4.5)/(9)`.

i.e.
`a=0.5`.

Hence, the equation that models this path is
`y=0.5(x+1)^(2)-1.5`.