Acoordinate grid is mapped on a video game screen, with the origin in the lower-left corner. a game designer programs a helicopter to follow a path that can be modeled by a quadratic function with a vertex at (16, 20) and passing through the point (4, 25). she also programs an airplane to move along a linear path that passes through the points (0, 18) and (30, 20). which system of equations can be used to determine whether the paths of the helicopter and airplane cross? mc017-1.jpg mc017-2.jpg mc017-3.jpg mc017-4.jpg

Find the equations then set them equal to each other

y=a(x-h)^2+k
quadracit (h,k) is vertex
helicopeter
vertex at (16,20)
y=a(x-16)^2+20
a point is (4,25)
25=a(4-16)^2+20
25=a(-12)^2+20
25=a(144)+20
minus 20 both sides
5=a(144)
divide both sides by 155
5/144=a
y=(5/144)(x-16)^2+20

airplane
y=mx+b
m=slope
b=yint
slope=(y2-y1)/(x2-x1)
slope=(20-18)/(30-0)=2/30=1/15
y=1/15x+b
(0,18)
18=1/15(0)+b
18=b
y=1/15x+18

we have
y=(5/144)(x-16)^2+20
and
y=1/15x+18
set equal to each other and solve for x value
(5/144)(x-16)^2+20=1/15x+18
after some work
and disregard the negative value since that is not allowed
x=40.413
plug in
y=1/15(40.413)+18
y=20.6942

they cross at (40.413,20.6942)