Find a function whose graph is a parabola with verrtex (2,-9) and that paasses through the point (3,-5).

Solution:

y = a(x-2)^2 -9

x = 3, y = a-9 = -5, a = 4

So y =4(x-2)^2 -9

Find the domain and range of the funtion f(x)=x^2-10x+1

Solution:

Domain: R

Range: [-24, +oo)

Find the maxiumum valueof the function f(x)=-x^4

Solution:

Max = 0, x=0

Suspose that g(x)=3x+1 and h(x)=9x^2+6x+7. Find a funtion f(g(x))=h(x).

Solution:

f(3x+1)=9x^2+6x+7 = (3x+1)^2 + 6

f(x)=x^2 +6

An airplane is flying at a speed of 450 mph at an altitude of h miles. The plane passes directly above a radar station at time t = 0.Express the distance (in miles) between the plane and the radar station as a function of time t (in hours) that the plane has flown if h = 2.

Solution:

The equation is

Distance: D

Time: t

D = sqrt[(450t)^2 + 2^2]