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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?

Respuesta :

Answer:

[tex]y=0.5(x+1)^{2} -1.5[/tex]

Step-by-step explanation:

We know that,

The equation representing the quadratic function having the vertex ( h,k ) is given by [tex]y=a(x-h)^{2}+k[/tex].

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

[tex]y=a(x+1)^{2}-1.5[/tex].

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

[tex]3=a(2+1)^{2}-1.5[/tex].

i.e. [tex]3=a3^{2}-1.5[/tex].

i.e. [tex]3=9a-1.5[/tex].

i.e. [tex]9a=3+1.5[/tex].

i.e. [tex]9a=4.5[/tex].

i.e. [tex]a=\frac{4.5}{9}[/tex].

i.e. [tex]a=0.5[/tex].

Hence, the equation that models this path is [tex]y=0.5(x+1)^{2}-1.5[/tex].

mockingjay2649

Answer:

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

Step-by-step explanation:

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