Answer:
Take the coordinates of each vertex (corner point) and subtract 2 from the x-coordinate; leave the y-coordinate alone.
Step-by-step explanation:
Example: If one vertex is the point (5, 3), then it moves left 2 units to (3, 3).
If a vertex is at (-3, 1), then it moves 2 units left to (-5, 1).
6.3 many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks
<u>Step-by-step explanation:</u>
We have , Trenton and Maria record how much dry food their pets eat on average each day.• Trenton's pet: 4/5 cup of dry food• Maria's pet: 1.25 cups of dry food. Based on these averages . We need to find how many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks . We need to find how much they eat for 14 days as:
Trenton's pet: 4/5 cup of dry food•
With 4/5 per day , for 14 days :
⇒ ![14(\frac{4}{5} )](https://tex.z-dn.net/?f=14%28%5Cfrac%7B4%7D%7B5%7D%20%29)
⇒ ![14(0.8 )](https://tex.z-dn.net/?f=14%280.8%20%29)
⇒ ![11.2](https://tex.z-dn.net/?f=11.2)
Maria's pet: 1.25 cups of dry food.
With 1.25 per day , for 14 days :
⇒ ![14(1.25 )](https://tex.z-dn.net/?f=14%281.25%20%29)
⇒ ![17.5](https://tex.z-dn.net/?f=17.5)
Subtracting Maria's - Trenton's :
⇒ ![17.5-11.2=6.3](https://tex.z-dn.net/?f=17.5-11.2%3D6.3)
That means , 6.3 many more cups of dry food will Maria's pet have eaten than Trenton's pet will have eaten over 2 seven-day weeks
if you want to come bird 5 pints to 3 quarts it's 2.5 quarts
first you do 8×12=92 then you do 92+2=94 94×12=1,128 so you save1,128 if I'm not wrong
The quadratic function given by:
is in vertex form. The graph of
is a parabola whose axis is the vertical line
and whose vertex is the point
. So:
To translate the graph of a function to the right, left, upward or downward we have:
![For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)](https://tex.z-dn.net/?f=For%20%5C%20a%20%5C%20positive%20%5C%20real%20%5C%20number%20%5C%20c.%20%5C%20%5Cmathbf%7BVertical%20%5C%20and%20%5C%20horizontal%20%5C%20shifts%7D%20%5C%5C%20in%20%5C%20the%20%5C%20graph%20%5C%20of%20%5C%20y%3Df%28x%29%20%5C%20are%20%5C%20represented%20%5C%20as%20%5C%20follows%3A%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Vertical%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20%5Cmathbf%7Bupward%7D%3A%20%5C%5C%20g%28x%29%3Df%28x%29%2Bc%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Vertical%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20%5Cmathbf%7Bdownward%7D%3A%20%5C%5C%20g%28x%29%3Df%28x%29-c%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Horizontal%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20to%20%5C%20the%20%5C%20%5Cmathbf%7Bright%7D%3A%20%5C%5C%20g%28x%29%3Df%28x-c%29%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20Horizontal%20%5C%20shift%20%5C%20c%20%5C%20units%20%5C%20to%20%5C%20the%20%5C%20%5Cmathbf%7Bleft%7D%3A%20%5C%5C%20g%28x%29%3Df%28x%2Bc%29)
By knowing this things, we can solve our problem as follows:
FIRST.
- Translating <em>11 units to the left:</em>
![g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%2B11%29%20%5C%5C%20%5C%5C%20%5Ctherefore%20g%28x%29%3D%28x%2B11%29%5E2)
- Then translating<em> 5 units down:</em>
![g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29-c%20%5C%5C%20%5C%5C%20%5Ctherefore%20g%28x%29%3D%28x%2B11%29%5E2-5)
Since the new function is fatter, the factor we need to multiply the term
<em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.
<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>
SECOND.
- Translating <em>8 units to the right:</em>
![g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2](https://tex.z-dn.net/?f=g%28x%29%3Df%28x-8%29%20%5C%5C%20%5C%5C%20%5Ctherefore%20g%28x%29%3D%28x-8%29%5E2)
- Then translating<em> 1 unit down:</em>
![g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29-c%20%5C%5C%20%5C%5C%20%5Ctherefore%20g%28x%29%3D%28x-8%29%5E2-1)
As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.
<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>