To find an equation for the path of the baseball, we can use quadratic regression since the data appears to follow a quadratic pattern. We'll use the general quadratic equation:
y = ax^2 + bx + c
Now, we need to determine the values of the coefficients a, b, and c. We can do this by substituting the given data points into the equation.
Using the data point (0.5, 18):
18 = a(0.5)^2 + b(0.5) + c
Using the data point (1, 24):
24 = a(1)^2 + b(1) + c
Using the data point (1.5, 22):
22 = a(1.5)^2 + b(1.5) + c
Using the data point (2, 12):
12 = a(2)^2 + b(2) + c
Now, you have a system of four equations with three unknowns (a, b, and c). Solve this system to find the coefficients a, b, and c. Once you have these coefficients, you can write the equation for the path of the baseball.
After solving for a, b, and c, the equation for the path of the baseball should be something like:
y = ax^2 + bx + c
Now, to find the height of the baseball after 1.7 seconds, simply plug in x = 1.7 into the equation and solve for y:
y = a(1.7)^2 + b(1.7) + c
Substitute the values of a, b, and c that you found earlier, and calculate y to find the height after 1.7 seconds.