Red bird starts his flight from points (10,0). His flight path reaches a maximum height of 18 yards and lands at points (38,0).
1) What is the maximum height of the red bird in yards?
2)What is the axis of symmetry of RED bird?
3)What is the total distance RED bird traveled (in yards)?
4)What is the equation for RED bird's distance traveled (equation should be in vertex form)?

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; link

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

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step-by-step explanation: