30points

1) the function f(x) varies directly with x and f(x)= 160 when x=40. what is f(x) when x=8?
a)32
b)20
c)5
d)2
2)the function f(x) varies inversely with x and f(x)=2 when x=16. what is f(x) when x=4?
a 128
b 72
c 40
d 8
3)the pressure of a gas p(v) varies inversely with the volume of the gas v. the pressure of a gas measures 15kg/cm² when its volume is 300cm³. which equation can be used to find the pressure of the gas when the volume is changed?
a p(v)=20v
b p(v)=20/v
c p(v)=4500v
d p(v)=4500/v
4)the scale factor of the blueprimt of a shopping mall to the actual shopping mall is 1in/18ft. the area of the mall on the blueprint is 190in². what is the area of the actual shopping mall?
a 61,560ft²
b 36,118ft²
c 6840ft²
d 3420ft²
5)the scale factor of a model of a grain silo to the actual silo is 1 to 10. the volume of the actual silo is 550m³. what is the volume of the model?
a 0.55m³
b 2.75m³
c 5.5m³
d 27.5m³

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1