Expert: Richard J. Raridon - 8/10/2007

Question
state the domain range of -3f(x)

state the domain range of y=1/(x+3)

find the inverse of each function.
f={(-5,-3), (-3,-2), (-1,-1), (1,0), (3,1)}
f(x)=x+3
f(x)=(x-1)^2+2

state the domain of range of f-1(x),
givenf(x)=x+3f(x)=(x-1)^2+2


state the nature of the root by finding the discriminant then find the roots.
y=x^2-6x-7
y=3x^2-2x+1
y=x^2+4x+1
y=-2x^2-x+1

a movie theatre sells tickets @ $8.50 each. the manger wants to raise prices but knows that for every 50cents the price is raised 20 fewer people go to the movies. the equation R=-40c^2-720c describes the relationship between cost of tickets, c dollars, and amount of revenue, R dollars, that the theatre makes. what price should the theatre charge to maximize revenue?

a football player attempts a field goal by kicking the football. the ball follows the path modelled by the equation h=4.9t^2+10t+3, where h is the height of the ball above the grounds in meters, t is the time since the ball was kicked in seconds.

describe the path of the ball?

after how many seconds does the ball reach the ground?the ball must clear the uprights for the field goal to count. the uprights are 5 m high. How long does the ball stay above 5 m in height?

find the equation of a quadratic that has 3 + i and 3 - i as its roots?

find the vertex of each quadratic equation

y=x^2-4x+3
y=x^2-6x+9
y=-x^2-3

Answer
I don't do domains and inverses.
y = x^2-6x-7, 64, x = 7, -1
y = 3x^2-2x+1, -12, x = 1/3 +i(2^1/2), 1/3 -i(2^1/2)
y = x^2+4x+1, 12, x = -2 +3^1/2, -2 -3^1/2
y = -2x^2-x+1, 9, x = 1/2, -1
R = -40c^2 -720c can't be the correct equation since it is negative for every value of c
h = 4.9t^2 +10t+3 is incorrect.  It should be
h = -4.9t^2 +10t +3 which is a parabola.
for h = 0, t = 2.306s
for h = 5, t = 0.225s, 1.816s for a difference of 1.591s
3+i and 3-i are the roots of x^2-6x+10
y = x^2-4x+3, (2,-1)
y = x^2-6x+9, (3,0)
y = -x^2-3, (-3,0)