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

Y = -0.005x^2 + x + 3

A. h = Xv = -b / 2a = -1 / -0.01 = 100 X = 100 = Eq of axis of symmetry.

B. The max ht = Y-coordinate of vertex.
In the given Eq, substitute 100 for X
and get: Yv = K = 53 = max ht.

V(h,k) = V(100,53).

C. Y = -0.005x^2 + x + 3 = 3,
-0.005x^2 + x = 3-3 = 0,
x(-0.005x + 1) = 0,

X = 0,
-0.005x + 1 = 0,
0.005x = 1,
X = 200 = Hor. distance traveled.

A. The equation for the axis of symmetry can be found using the formula: x = -b/2a, where a and b are the coefficients in the quadratic equation. In this case, a = -0.005 and b = 1. So, the equation of the axis of symmetry is x = -1/(2*-0.005) = -100. Great job, you got it right!

B. To find the maximum height reached by the baseball, we can use the equation h = -0.005x^2 + x + 3, where h represents the height. Since the equation is in the form of a quadratic function, the vertex represents the maximum height. To find the x-coordinate of the vertex, we can use the formula mentioned earlier: x = -b/2a. For this equation, the x-coordinate of the vertex is -1/(2*-0.005) = 100. Now, substitute the x-coordinate into the equation to find the maximum height: h = -0.005(100)^2 + 100 + 3. Calculate that out and you'll get your answer!

C. To find the horizontal distance the ball has traveled when the outfielder catches it, we need to set the height (h) equal to 3 feet (since the outfielder catches the ball 3 ft above the ground). Plug in h = 3 into the equation h = -0.005x^2 + x + 3 and solve for x.

A. To find the equation of the axis of symmetry, we need to use the formula x = -b/(2a), where a and b are coefficients in the quadratic equation.

In this case, the equation of the path of the ball is h = -0.005x^2 + x + 3.

Comparing this equation to the standard quadratic equation form (ax^2 + bx + c), we find that a = -0.005 and b = 1.

Using the formula x = -b/(2a), we can calculate the equation of the axis of symmetry as follows:

x = -(1) / (2 * (-0.005))
x = 100

So, 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 formula is given as (-b/(2a), f(-b/(2a))), where f(x) is the function of the quadratic equation.

In this case, the equation of the path of the ball is h = -0.005x^2 + x + 3.

Using the vertex formula, we can calculate the maximum height as follows:

x = -(1) / (2 * (-0.005))
x = 100

To find the corresponding height, we substitute this value of x into the equation:

h = -0.005(100)^2 + (100) + 3
h = -0.005(10,000) + 100 + 3
h = -50 + 103
h = 53

Therefore, the maximum height reached by the baseball is 53 feet.

C. To determine how far the ball has traveled horizontally when the outfielder catches it at a height of 3 feet, we need to solve for x in the equation:

h = -0.005x^2 + x + 3

Substituting the value of h as 3, the equation becomes:

3 = -0.005x^2 + x + 3

Re-arranging the equation to standard quadratic form:

0 = -0.005x^2 + x

0 = x(-0.005x + 1)

Solving for x, we find two possible solutions:

x = 0
or
-0.005x + 1 = 0
-0.005x = -1
x = -1/(-0.005)
x = 200

Since the distance cannot be negative, we take the positive value, x = 200.

Therefore, the ball has traveled 200 feet horizontally when the outfielder catches it.

A. To find the equation of the axis of symmetry, you can use the formula x = -b/2a. In this case, a is -0.005 and b is 1. Plugging these values into the formula gives:

x = -1 / (2 * -0.005)
x = 100

Therefore, the equation of the axis of symmetry is x = 100. So, your answer is incorrect. The axis of symmetry is not -100, but rather 100 (which represents the horizontal distance).

B. To find the maximum height reached by the baseball, you need to find the vertex of the parabola defined by the equation. The formula for the x-coordinate of the vertex is -b/2a. Since b is 1 and a is -0.005, plugging these values into the formula gives:

x = -1 / (2 * -0.005)
x = 100

Now, substitute this x-value back into the equation to find the height:

h = -0.005 * (100)^2 + (100) + 3

Calculating this gives:

h = -0.005 * 10000 + 100 + 3
h = -50 + 100 + 3
h = 53

Therefore, the maximum height reached by the baseball is 53 feet.

C. To find out how far the ball has traveled when the outfielder catches it, we need to set the height (h) in the equation equal to 3 feet (since the outfielder catches it 3 feet above the ground) and solve for x. The equation becomes:

3 = -0.005x^2 + x + 3

Rearrange the equation to be in standard quadratic form:

0.005x^2 - x = 0

Now, you can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Whichever method you choose, you'll find the values for x (horizontal distance).

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