Answer:
Step-by-step explanation:
Any point on a given parabola is equidistant from focus and directrix.
Given:
Focus of the parabola is at 
.
Directrix of the parabola is 
.
Let 
be any point on the parabola. Then, from the definition of a parabola,
Distance of from focus = Distance of from directrix.
Therefore,
Squaring both sides, we get
![(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9](https://tex.z-dn.net/?f=%28x-2%29%5E%7B2%7D%2B%28y-8%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D-%28y-8%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%2By-8%29%28y-10-%28y-8%29%29...............%5B%5Cbecause%20a%5E%7B2%7D-b%5E%7B2%7D%3D%28a%2Bb%29%28a-b%29%5D%5C%5C%28x-2%29%5E%7B2%7D%3D%282y-18%29%28y-10-y%2B8%29%5C%5C%28x-2%29%5E%7B2%7D%3D2%28y-9%29%28-2%29%5C%5C%28x-2%29%5E%7B2%7D%3D-4%28y-9%29%5C%5Cy-9%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%5C%5Cy%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%2B9)
Hence, the equation of the parabola is .
Answer:
g-1(x) = 3(x + 7).
Domain is All Real values of x.
Range is All Real values of the function.
Step-by-step explanation:
Let y = 1/3 x - 7
1/3 x = y + 7
Multiply both sides by 3:
x = 3(y + 7)
So the inverse of g(x) = g-1(x) = 3(x + 7).
Domain is All Real values of x.
Range is All Real values of the function.
Step-by-step explanation:
l = 3x - 5
w = 2x + 9
perimeter = 2l + 2w = 2(3x - 5) + 2(2x + 9) =
= 6x - 10 + 4x + 18 = 10x + 8
area = l×w = (3x - 5)(2x + 9) = 6x² + 27x - 10x - 45 =
= 6x² + 17x - 45
JfpeiJKFHGIFWjfowednklsv WEOIHGVFOEWDBISFKCJPFGVUOEIDSVB PIFGHFIAGHRKFNBLKGVBJ;ALKFBGO'klVFBFJSKDGPV;KFJDZNBAJGIJGJNVL;ZGJEORITUJLDNVZ;.JDFG[OAEJRGNA'JGBj'gaklrfmgo'ajgb'pzang'ajrebgmkza'pgjozn;klfdbgkl'fznkp'fgnko'lgkfv.
Answer:
Step-by-step explanation:
Given: 
To find: average rate of change of the function over the interval 
and 
Solution:
Take 
Find 
Average rate of change of the function 
