Jose bautista hits a baseball that travels for 142m before it lands. The flight of the ball can be modelled by a quadratic function in which x is the Horizontal distance the ball has travelled away from jose, and h(x) is the height Vertical distance of the ball at that distance.

1. Assume that the ball was between 0.6m and 1.5m above the ground when it was hit.
a) what would h(142) be?
b) what happens when x=0? What are some possible values for h(x) when x=0
Sorry if someone could even just give me tips on how to do this, I'm so lost.

h(x) = ax^2+bx+c

h(142) = 0, because at that distance the ball hits the ground

h(0) is the initial height when the ball was hit (it has not traveled any distance yet). So, 0.6 <= h(0) <= 1.5

HAHA I need help with that too and i think we are in the same class (*CCH right)

PS. posted if you know the answer

the answer to c) and d)

To solve this problem, we will use the given information to find the quadratic function representing the height of the ball and use it to answer the questions.

Let's assume the quadratic function is of the form h(x) = ax^2 + bx + c, where x is the horizontal distance in meters and h(x) is the height of the ball in meters.

To find the quadratic function, we need to determine the values of the coefficients a, b, and c.

From the given information, we know:
- When the ball was hit, it was between 0.6m and 1.5m above the ground. This gives us the initial condition: h(0) is between 0.6 and 1.5.

Since we are given the horizontal distance the ball traveled (142m) before landing, we can use this information to determine the value of h(142).

Now, let's address each question step by step:

a) To find h(142), we need to plug in x = 142 into the quadratic function h(x) = ax^2 + bx + c and solve for h(142). However, we don't have the values of a, b, and c yet.

To find these coefficients, we need more information. We can use the initial condition h(0) to solve for c. Let's say h(0) = k, where k is any value between 0.6 and 1.5.

Now we have the following:
h(0) = a(0)^2 + b(0) + c = c = k

So, we know that c = k.

Now we can write our quadratic function as h(x) = ax^2 + bx + k.

b) When x = 0 (which represents the starting point), we can find the possible values of h(x) by substituting x = 0 into the quadratic function h(x) = ax^2 + bx + k:

h(0) = a(0)^2 + b(0) + k = k

Therefore, when x = 0, h(x) can be any value equal to k, where k is between 0.6 and 1.5.

Now that we have the form of the quadratic function as h(x) = ax^2 + bx + k, we can proceed to find h(142) by substituting x = 142:

h(142) = a(142)^2 + b(142) + k

Unfortunately, without further information or additional conditions, we cannot calculate the exact value of h(142) because we do not know the values of a and b.

To find the values of a and b, we would either need additional information, such as another point on the graph, or some physical understanding of the situation (e.g., the maximum height reached by the ball and its x-coordinate).

I hope this explanation helps guide you through the problem. If you have any further questions, please, let me know!