Distance between A and B
= Distance between C and D
= sqrt((4 - 1)^2 + (5 - 2)^2)
= sqrt(3^2 + 3^2)
= sqrt(2 * 3^2)
= sqrt(3^2) * sqrt(2)
= 3sqrt(2)
Distance between B and C
= Distance between A and D
= sqrt((4 - 3)^2 + (5 - 0)^2)
= sqrt(1^2 + 5^2)
= sqrt(26)
Since sqrt(26) is more than 3sqrt(2), the length must be sqrt(26).
Hope this helps you.
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k
nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix
I will only convert the 1st one fully, you should be able to do the rest
1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
(-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)
k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5
basically completee the square with x and find P by force factoring a 4 out
2. directix: y=-1.75
3. directix: y=1.5
4. directix: y=17.25
5. d: -37.5
6. d: 9.25
7. d=2.625
order them yourself
Percent change=change/original times 100
chane=28-23=5
oriiginal=28
percent change=5/28 times 100
0.178 times 100
17.8
about 18% change
Just subtract 32, then divide by 9/5 (or multiply by the reciprical) then add 273.15.
K=5/9(F-32)+273.15
