Answer:
A function to represent the height of the ball in terms of its distance from the player's hands is 
Step-by-step explanation:
General equation of parabola in vertex form 
y represents the height
x represents horizontal distance
(h,k) is the coordinates of vertex of parabola
We are given that The ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.
So,(h,k)=(18,12)
Substitute the value in equation
---1
The ball leaves the player's hands at a height of 6 feet above the ground and the distance at this time is 0
So, y = 6
So,
6=324a+12
-6=324a
Substitute the value in 1
So,
Hence a function to represent the height of the ball in terms of its distance from the player's hands is
Answer:
56
Step-by-step explanation:
1. A polynomial function is a function that can be written in the form
f(x)=anxn +an−1xn−1 +an−2xn−2 +...+a2x2 +a1x+a0,
where each a0, a1, etc. represents a real number, and where n is a natural number Here are the steps required for Solving Polynomials by Factoring:
Step 1: Write the equation in the correct form. To be in the correct form, you must remove all parentheses from each side of the equation by distributing, combine all like terms, and finally set the equation equal to zero with the terms written in descending order.
Step 2: Use a factoring strategies to factor the problem.
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
Example 1 – Solve: 3x3 = 12x
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.
Step 1
Step 2: Use a factoring strategies to factor the problem.
Step 2
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
Step 3
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
Step 4
Example 2 – Solve: x3 + 5x2 = 9x + 45
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.
Step 1
Step 2: Use a factoring strategies to factor the problem.
Step 2
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
Step 3
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
Step 4
Click Here for Practice Problems
Example 3 – Solve: 6x3 – 16x = 4x2
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.
Step 1
Step 2: Use a factoring strategies to factor the problem.
Step 2
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
Step 3
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
Step 4
Click Here for Practice Problems
Example 4 – Solve: 3x2(3x + 4) = 12x(x + 3)
Step 1: Write the equation in the correct form. In this case, we need to remove all parentheses by distributing and set the equation equal to zero with the terms written in descending order.
Step 1
Step 2: Use a factoring strategies to factor the problem.
Step 2
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
Step 3
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
Step 4
Click Here for Practice Problems
Example 5 – Solve: 16x4 = 49x2
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.
Step 1
Step 2: Use a factoring strategies to factor the problem.
Step 2
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
Step 3
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
Step 4
Click Here for Practice Problems
Check the picture below.
as we can see in the picture, the lengths for YZ and ZX are very straight, let's get the side YX
![~~~~~~~~~~~~\textit{distance between 2 points} \\\\ Y(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad X(\stackrel{x_2}{2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ YX=\sqrt{[2 - 0]^2 + [4 - (-2)]^2}\implies YX=\sqrt{2^2+(4+2)^2} \\\\\\ YX=\sqrt{4+6^2}\implies YX=\sqrt{40} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{2~~+~~6~~+~~\sqrt{40}~~\approx~~14.32} ~\hfill \stackrel{\textit{\Large Area}}{\cfrac{1}{2}(2)(6)\implies 6}](https://tex.z-dn.net/?f=~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20Y%28%5Cstackrel%7Bx_1%7D%7B0%7D~%2C~%5Cstackrel%7By_1%7D%7B-2%7D%29%5Cqquad%20X%28%5Cstackrel%7Bx_2%7D%7B2%7D~%2C~%5Cstackrel%7By_2%7D%7B4%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20YX%3D%5Csqrt%7B%5B2%20-%200%5D%5E2%20%2B%20%5B4%20-%20%28-2%29%5D%5E2%7D%5Cimplies%20YX%3D%5Csqrt%7B2%5E2%2B%284%2B2%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20YX%3D%5Csqrt%7B4%2B6%5E2%7D%5Cimplies%20YX%3D%5Csqrt%7B40%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7B%5CLarge%20Perimeter%7D%7D%7B2~~%2B~~6~~%2B~~%5Csqrt%7B40%7D~~%5Capprox~~14.32%7D%20~%5Chfill%20%5Cstackrel%7B%5Ctextit%7B%5CLarge%20Area%7D%7D%7B%5Ccfrac%7B1%7D%7B2%7D%282%29%286%29%5Cimplies%206%7D)
Answer:
f ∘ g(5) = 47
Step-by-step explanation:
We are given the following functions:
Composite function:
The problem asks their composite function at x = 5. So
We have that f ∘ g(5) = 47
