An archer releases an arrow from a shoulder height of 1.39 m. When

the arrow hits the target 18 m away, it hits point A. When the target is
removed, the arrow lands 45 m away. Find the maximum height of the arrow along its parabolic path.
My points are
(0,1.39)
(18,1.5)
(45,0)
I'm supposed to use this formula: y = ax^2 + bx + c
I get C = 1.39 after that I get lost

ax^2+bx+c=y

0a+0b+c=1.39
324a+18b+c=1.5
2025a+45b+c=0

a=-.00137
b=0.0308
c=1.39

y = -.00137x^2 + 0.031x + 1.39

max height on the parabola is at x = -b/2a, so at
x = .031/.00274 = 11.31
y = 1.565

To find the maximum height of the arrow along its parabolic path, we need to determine the values of a, b, and c in the equation y = ax^2 + bx + c, using the given points.

We know that the vertex of the parabola represents the maximum height, and its x-coordinate will give us the value of x when the arrow reaches its maximum height.

Let's plug in the coordinates (0, 1.39) and (18, 1.5) into the equation and form a system of two equations to solve for a and b.

1. When x = 0, y = 1.39:
1.39 = a(0)^2 + b(0) + c
1.39 = c ...(1)

2. When x = 18, y = 1.5:
1.5 = a(18)^2 + b(18) + c
1.5 = 324a + 18b + c ...(2)

Since we have found that c = 1.39 in equation (1), we can substitute this value into equation (2) and solve for a and b.

1.5 = 324a + 18b + 1.39
0.11 = 324a + 18b ...(3)

Now, we can use the third given point (45, 0) to form another equation.

3. When x = 45, y = 0:
0 = a(45)^2 + b(45) + c
0 = 2025a + 45b + 1.39 ...(4)

We will use equations (3) and (4) to solve for a and b.

Subtracting equation (3) from equation (4):
2025a + 45b + 1.39 - (324a + 18b) = 0

Simplifying the equation:
1701a + 27b = -1.39 ...(5)

We now have a system of two equations: equation (3) and equation (5).

Now, we can solve this system of equations to find the values of a and b. Once we have a and b, we can substitute them back into equation (1) to find the value of c, which will complete the equation y = ax^2 + bx + c.

Solving this system of equations will give us the values of a, b, and c, which will allow us to determine the maximum height of the arrow along its parabolic path.