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].
Answer:
y = 0.5(x - (-1)^2 + (-1.5)
Step-by-step explanation:
