What are the values of the constants in the vertex form of the quadratic equation that models the bird's path? $$ h=0 $$ $$ k=0 $$ $$ a=40 $$ CompLETE Which system of equations could you use to deternine where the paths intersect? $$ \quad y=0 $$ and $$ y=-0.12(x-20)^{2} $$ $$ \quad y=0.8 x $$ and $$ y=-0.12 x^{2}+20 $$ $$ y=0.8 x $$ and $$ y=-0.12(x-20)^{2} $$ $$ y=0.8 x+8 $$ and $$ y=-0.12 x^{2}+20 $$ DONE 8

Question

UpStudy AI · Accepted Answer

1. The quadratic model for the bird’s path is written in vertex form as  
  $$
  y = a(x-h)^2 + k.
  $$  
According to the problem, the constants are given by  
  $$
  h = 0,\quad k = 0,\quad a = 40.
  $$

2. To determine the point(s) at which the bird’s path meets the other path, we set up a system where one equation is the bird’s quadratic path and the other is the equation for the second path. One of the answer choices uses a quadratic in vertex form. Notice that the choice  
  $$
  y = -0.12(x-20)^2
  $$  
expresses a quadratic in vertex form, and it’s paired with the linear equation  
  $$
  y = 0.8x.
  $$  
Since solving for the intersection involves equating the two expressions for $$ y $$, the system  
  $$
  \begin{cases}
  y = 0.8x, \
  y = -0.12(x-20)^2,
  \end{cases}
  $$  
is the set of equations you can use to determine where the paths intersect.

Thus, the correct system of equations is  
  $$
  y = 0.8x \quad \text{and} \quad y = -0.12(x-20)^2.
  $$
To find where the bird's path intersects another path, use the system of equations: $$ y = 0.8x \quad \text{and} \quad y = -0.12(x-20)^2 $$

What are the values of the constants in the vertex
form of the quadratic equation that models the
bird’s path?

CompLETE
Which system of equations could you use to
deternine where the paths intersect?
and
and
and
and
DONE 8

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What are the values of the constants in the vertex form of the quadratic equation that models the bird’s path? CompLETE Which system of equations could you use to deternine where the paths intersect? and and and and DONE 8