Answer:
Seems like someone answered them, because the red writing is right, but here's the answers with explanation
Step-by-step explanation:
- The vertex is the point at which the graph changes direction as we go from left to right.
- Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.
- Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started rising
- Now the answers:
- Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so <em>minimum</em>
- vertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so <em>minimum</em>
- vertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is <em>maximum</em>
- Vertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is <em>maximum</em>
- vertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is <em>minimum</em>
- vertex is (0.5,5) because it was getting big then changed and started getting smaller so <em>maximum</em>
A=P(1+r/n)^(tn)
n=number of times per year compounded
A=amount
P=principal inveseted
r=rate in decimal
t=time in years
so
we want A=30000
r=12.4%=0.124
t=15
monthyl means n=12
30000=P(1+0.124/12)^(15*12)
solve for P
easy, just divide both sides by (1.01033)^180
4714.97=P
that much must be invested
Answer:4
Step-by-step explanation:
A zero-coupon bond doesn’t make any payments. Instead, investors purchase the zero-coupon bond for less than its face value, and when the bond matures, they receive the face value.
To figure the price you should pay for a zero-coupon bond, you'll follow these steps:
Divide your required rate of return by 100 to convert it to a decimal.
Add 1 to the required rate of return as a decimal.
Raise the result to the power of the number of years until the bond matures.
Divide the face value of the bond to calculate the price to pay for the zero-coupon bond to achieve your desired rate of return.
First, divide 4 percent by 100 to get 0.04. Second, add 1 to 0.04 to get 1.04. Third, raise 1.04 to the sixth power to get 1.2653. Lastly, divide the face value of $1,000 by 1.2653 to find that the price to pay for the zero-coupon bond is $790,32.
Ho ho ho, lets get this party started
ok so I'm just really excited to use this stuff that I just learned
so
multiplicites
if a root or zero has an even multilicity, the graph bounces on that root
if the root or zero has an odd multiplicty, the graph goes through that root
so
roots are
-1
2
4
multiplicty is how many times it repeats
2 has even multiplity
we just do 2 is odd and 1 is even so
for roots, r1 and r2, the facotrs would be
(x-r1)(x-r2)
so
(x-(-1))^1(x-2)^2(x-4)
(x+1)(x-2)^2(x-4)
this is a 4th degre equaton
normally, it is goig from top right to top left
it is upside down
theefor it has negative leading coefient
y=-k(x+1)(x-4)(x-2)^2