A baseball player hits a baseball into the outfield. The equation h= -0.005x^2 +x+3 give the path of the ball, where (h) is the height and (x) is the horizontal distance the ball travels.

A. What is the equation of the axis of symmetry? It's -100 right?
B. What is the Mac height reached by the baseball? Idk
C. An outfielder catches the ball 3 ft above the ground. How far has the ball traveled horizontally when the outfielder catches it? Idk

A. The equation for the axis of symmetry can be found using the formula x = -b/2a, where a, b, and c are the coefficients in the quadratic equation. In this case, a = -0.005 and b = 1. Plugging these values into the formula, we get x = -1/(2*(-0.005)). Simplifying this equation gives x = -1/(-0.01) = 100, so the axis of symmetry is x = 100.

B. To find the maximum height reached by the baseball, we need to determine the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the same formula from part A, which gives us x = 100. Plugging this value into the equation h = -0.005x^2 + x + 3 gives us h = -0.005(100)^2 + 100 + 3 = -0.005(10000) + 100 + 3 = -50 + 100 + 3 = 53. Therefore, the maximum height reached by the baseball is 53 feet.

C. To find how far the ball has traveled horizontally when the outfielder catches it, we need to substitute h = 3 into the equation h = -0.005x^2 + x + 3 and solve for x. Setting 3 = -0.005x^2 + x + 3, we get -0.005x^2 + x = 0. Rearranging this equation, we have -0.005x^2 + x - x = 0, which simplifies to -0.005x^2 = 0. Dividing both sides by -0.005, we get x^2 = 0. Now taking the square root of both sides, we get x = 0. Therefore, the ball has traveled 0 feet horizontally when the outfielder catches it.

A. The equation of the axis of symmetry can be found using the formula x = -b / (2a), where the equation is in the form ax^2 + bx + c. In this case, the equation is h = -0.005x^2 + x + 3. Comparing this with the standard quadratic equation form, we can see that a = -0.005 and b = 1. Plugging these values into the formula, we get x = -(1) / (2*(-0.005)) = -1 / (-0.01) = 100. Therefore, the equation of the axis of symmetry is x = 100.

B. To find the maximum height reached by the baseball, we need to determine the vertex of the quadratic equation. The vertex can be found using the formula x = -b / (2a) and then plugging this value into the equation to find the corresponding height (h).

Using the same formula as in part A, we can find that x = 100. Plugging this value into the equation h = -0.005(100)^2 + 100 + 3, we get the maximum height as h = 3. Therefore, the maximum height reached by the baseball is 3 units.

C. To determine the horizontal distance the ball has traveled when the outfielder catches it, we need to solve the quadratic equation h = -0.005x^2 + x + 3 for h = 3 (since the outfielder catches the ball at a height of 3 ft).

By substituting h = 3 into the equation, we get 3 = -0.005x^2 + x + 3. Rearranging the equation, we have -0.005x^2 + x = 0. Solving for x, we can use factoring or the quadratic formula. Factoring yields x(0.005x - 1) = 0 which gives two possible solutions: x = 0 or x = 1/0.005 = 200.

Since x = 0 represents the starting point of the ball, we can conclude that the ball has traveled horizontally for 200 feet when the outfielder catches it.

A. To find the equation of the axis of symmetry, we can use the formula x = -b/2a. In this equation, a represents the coefficient of x^2, and b represents the coefficient of x.

In the given equation h = -0.005x^2 + x + 3, we can see that a = -0.005 and b = 1. Plugging these values into the formula x = -b/2a, we get x = -1/(2 * (-0.005)) = 100.

So, the equation of the axis of symmetry is x = 100, not -100.

B. To find the maximum height reached by the baseball, we need to determine the vertex of the parabolic function h = -0.005x^2 + x + 3. The formula for the x-coordinate of the vertex is x = -b/2a, which we have already calculated to be x = 100.

Now, to find the corresponding y-coordinate (or the maximum height), we substitute x = 100 into the equation h = -0.005x^2 + x + 3:

h = -0.005(100)^2 + (100) + 3 = -0.005(10,000) + 100 + 3 = -50 + 100 + 3 = 53.

Therefore, the maximum height reached by the baseball is 53 units (which could represent feet, meters, etc., depending on the context).

C. To determine how far the ball has traveled horizontally when the outfielder catches it (let's call it D), we can set the height h equal to the outfielder's height (3 feet).

So, we need to solve the equation -0.005x^2 + x + 3 = 3.

Manipulating the equation, we get -0.005x^2 + x = 0.

Factoring out x, we have x(-0.005x + 1) = 0.

Setting each term equal to zero, we have x = 0 (which means the ball has traveled 0 distance horizontally at the beginning) and -0.005x + 1 = 0.

Solving -0.005x + 1 = 0 for x, we get x = 200.

So, the ball has traveled 200 units of distance horizontally when the outfielder catches it (again, the actual unit could depend on the context, such as feet, meters, etc.).