ANSWER
![f(x)= \frac{1}{4} {(x - 1)}^{2}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B1%7D%7B4%7D%20%7B%28x%20-%201%29%7D%5E%7B2%7D%20)
EXPLANATION
Since the directrix is
![y = - 1](https://tex.z-dn.net/?f=y%20%3D%20-%201)
the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,
![(1,1)](https://tex.z-dn.net/?f=%281%2C1%29)
also means that the parabola will open upwards.
The equation of parabola with such properties is given by,
![{(x - h)}^{2} = 4p(y - k)](https://tex.z-dn.net/?f=%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%3D%204p%28y%20-%20k%29)
where
![(h,k)](https://tex.z-dn.net/?f=%28h%2Ck%29)
is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at
![(1, - 1)](https://tex.z-dn.net/?f=%281%2C%20-%201%29)
The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,
![h = \frac{1 + 1}{2} = 1](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B1%20%2B%201%7D%7B2%7D%20%3D%201)
and
![k = \frac{ - 1 + 1}{2} = 0](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B%20-%201%20%2B%201%7D%7B2%7D%20%3D%200)
The equation of the parabola now becomes,
![(x - 1) ^{2} = 4p(y - 0)](https://tex.z-dn.net/?f=%28x%20-%201%29%20%5E%7B2%7D%20%3D%204p%28y%20-%200%29)
![|p| = 1](https://tex.z-dn.net/?f=%20%7Cp%7C%20%3D%201)
Thus, the distance between the vertex and the directrix.
This means that,
![p = - 1 \: or \: 1](https://tex.z-dn.net/?f=p%20%3D%20-%201%20%5C%3A%20or%20%5C%3A%201)
Since the parabola opens up, we choose
![p = 1](https://tex.z-dn.net/?f=p%20%3D%201)
Our equation now becomes,
![{(x - 1)}^{2} = 4(1)(y - 0)](https://tex.z-dn.net/?f=%20%7B%28x%20-%201%29%7D%5E%7B2%7D%20%3D%204%281%29%28y%20-%200%29)
This simplifies to
![{(x - 1)}^{2} = 4y](https://tex.z-dn.net/?f=%20%7B%28x%20-%201%29%7D%5E%7B2%7D%20%3D%204y)
or
![y = \frac{1}{4} {(x - 1)}^{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%7B%28x%20-%201%29%7D%5E%7B2%7D%20)
This is the same as,
![f(x)= \frac{1}{4} {(x - 1)}^{2}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B1%7D%7B4%7D%20%7B%28x%20-%201%29%7D%5E%7B2%7D%20)
The correct answer is D .
Answer:
1.37 miles
Step-by-step explanation:
If she went along 1/10 of the trail, multiply that fraction times the length of the trail
1/10 * 13.7
13.7/10
Move the decimal 1 place to the left since we are dividing by 10
1.37 miles
One example is that you're given blueprints and you want to find out how large the object is in real life, rather than just on paper. The scale factor will help find those real life measurements. Let's say a house on paper is 2 inches long, and also let's say the scale factor is labeled "1 inch = 20 feet". This means the real life house is 2*20 = 40 feet long.
You could think of it as 1 inch = 20 feet, so 2 inches = 40 feet (multiply both sides by 2).
Scale factors are also used in maps. Look at the bottom corner of any map and it will show you how each distance on paper corresponds to a real life distance (in miles or kilometers maybe). Usually it shows a checkered "ruler" of sorts.
Answer:
C. 7/4 + √3i / 4.
Step-by-step explanation:
(1 + 2√-3) / (1 + √-3)
Since √-1 = i we have:
(1 + 2√3i) / (1 + √3i)
Multiply top and bottom by the conjugate (1 - √3i):
(1 + 2√3i)( (1 - √3i) / (1 + √3i) (1 - √3i)
= 1 - √3 i + 2√3 i + 6) ( 1 + 3)
= 7 +√3i / 4
= 7/4 + √3i / 4.