Nthe 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?

Step-by-step explanation:

We know that,

The equation representing the quadratic function having the vertex ( h,k ) is given by .

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

.

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

.

i.e. .

i.e. .

i.e. .

i.e. .

i.e. .

i.e. .

Hence, the equation that models this path is .

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

step-by-step explanation: