Answer:
Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Step-by-step explanation:
9514 1404 393
Answer:
y = -1/4x^2 -3/2x +3/4
Step-by-step explanation:
You know that vertex form is ...
y = (1/(4p))(x -h)^2 +k
for a focus-vertex distance of p and a vertex of (h, k).
Here, the focus-vertex distance is 2-3 = -1 (difference of y-coordinates), and the vertex is (h, k) = (-3, 3). This means the vertex form equation is ...
y = -1/4(x +3)^2 +3
Expanding the square gives ...
y = -1/4(x^2 +6x +9) +3
y = -1/4x^2 -3/2x +3/4
_____
<em>Additional comment</em>
The square of a binomial is ...
(x +a)^2 = x^2 +2ax +a^2
Answer:
Option B ![x=-2](https://tex.z-dn.net/?f=x%3D-2)
Step-by-step explanation:
we know that
The critical point of a function are the points on the graph of a function where the derivative is zero or the derivative does not exist.
we have
![f(x)=2x^{2}+8x-7](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E%7B2%7D%2B8x-7)
step 1
Take the derivative of the function
![f'(x)=4x+8](https://tex.z-dn.net/?f=f%27%28x%29%3D4x%2B8)
step 2
Set that derivative equal to 0 and solve for x. Each x value you find is known as a critical number
![f'(x)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D0)
![4x+8=0](https://tex.z-dn.net/?f=4x%2B8%3D0)
![4x=-8](https://tex.z-dn.net/?f=4x%3D-8)
![x=-2](https://tex.z-dn.net/?f=x%3D-2)
<em>Alternative Method</em>
The critical point of the quadratic equation is the vertex, because the function changes from decreasing to increasing at that point (In this problem the vertex is a minimum)
we have
![f(x)=2x^{2}+8x-7](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E%7B2%7D%2B8x-7)
Convert into vertex form
![f(x)+7=2x^{2}+8x](https://tex.z-dn.net/?f=f%28x%29%2B7%3D2x%5E%7B2%7D%2B8x)
![f(x)+7=2(x^{2}+4x)](https://tex.z-dn.net/?f=f%28x%29%2B7%3D2%28x%5E%7B2%7D%2B4x%29)
![f(x)+7+8=2(x^{2}+4x+4)](https://tex.z-dn.net/?f=f%28x%29%2B7%2B8%3D2%28x%5E%7B2%7D%2B4x%2B4%29)
![f(x)+15=2(x^{2}+4x+4)](https://tex.z-dn.net/?f=f%28x%29%2B15%3D2%28x%5E%7B2%7D%2B4x%2B4%29)
![f(x)+15=2(x+2)^{2}](https://tex.z-dn.net/?f=f%28x%29%2B15%3D2%28x%2B2%29%5E%7B2%7D)
![f(x)=2(x+2)^{2}-15](https://tex.z-dn.net/?f=f%28x%29%3D2%28x%2B2%29%5E%7B2%7D-15)
the vertex is the point (-2,-15)
therefore
The x-coordinate of the critical point is x=-2
Answer:
12
Step-by-step explanation:
8x1+8x0.5
8+4
12
12$ is the total cost
Given is a function f(x) and function g(x) is formed when f(x) is shifted 4 units to the right.
Since the transformation is on x-axis, so it would be g(x)= f(x+k).
Positive values of k shifts the original graph to the left and Negative values of the k shifts the original graph to the right.
'4 units to the right' means k = -4.
So, it would be g(x) = f(x-4).
Given f(x) = -[x]
Therefore g(x) = f(x-4) = -[x-4]
Hence, option C is correct i.e. g(x) = - [x - 4].