Respuesta :
Answer:
1) 18 yards
2) x = 24
3) 36 yards
4) y = (-9/98)(x - 24)² + 18
Step-by-step explanation:
The path is symmetrical about x = h
h = (10+38)/2 = 24
x = 24
Distance = 18 + 18 = 36
Vertex: (24,18)
y = a(x - 24)² + 18
At t = 10, y = 0
0 = a(10 - 24)² + 18
a = -18/14²
a = -18/196 = -9/98
y = (-9/98)(x - 24)² + 18
1) The maximum height of the red bird in yards is; 18 yards
2) The axis of symmetry of the RED bird is; x = 24 yards
3) The total distance that the RED bird traveled in yards is; 28 yards
4) The equation for the RED bird's distance traveled in vertex form is; y = -⁹/₉₈(x - 24)² + 18
1) We are told that his flight reaches a maximum height of 18 yards.
Thus;
Maximum height of the red bird = 18 yards
2) He started his flight from the point (10, 0) and lands at a point (38, 0)
Axis of symmetry is symmetrical about the x-axis. Thus;
Axis of symmetry; x = (x₁ + x₂)/2
Axis of symmetry; x = (10 + 38)/2
Axis of symmetry; x = 24
3) The total horizontal distance will be gotten by subtracting the x-coordinate of the take off point from the landing point.
Total horizontal distance = 38 - 10
Total horizontal distance = 28 yards
4) The equation for the RED bird's distance travelled is gotten from the general vertex form;
y = a(x - h)² + p
where;
h is x-coordinate of vertex
p is y-coordinate of vertex
We know that max height of y = 18 is the y-coordinate of vertex while axis of symmetry, x = 24 is the x-coordinate of vertex.
Thus;
y = a(x - 24)² + 18
At the start point of (10, 0), we can find a
0 = a(10 - 24)² + 18
-18 = 196a
a = -18/196
a = -⁹/₉₈
Thus;
y = -⁹/₉₈(x - 24)² + 18
Read more about vertex form of projectiles at; https://brainly.com/question/12446886
