SOLUTION: The function f(x)=a√(x-h) +k has a maximal domain of [2, ∞) and range of (- ∞,3]. its graph passes through the point (6,-3). Find the equation of this function in

Algebra ->  Functions -> SOLUTION: The function f(x)=a√(x-h) +k has a maximal domain of [2, ∞) and range of (- ∞,3]. its graph passes through the point (6,-3). Find the equation of this function in      Log On


   

Question 1078803: The function f(x)=a√(x-h) +k has a maximal domain of [2, ∞) and range of (- ∞,3]. its graph passes through the point (6,-3). Find the equation of this function in the form f(x)=a√(x-h) +k.
√ symbol mean square root.
the answers-3√(x-2) +3.
can you explain to me how to get the answers?
Found 2 solutions by MathLover1, yongweizhen:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=a%2Asqrt%28x-h%29+%2Bk+
h is the horizontal shift and k is the vertical shift
given:
has a maximal domain of [2, infinity) => means if x=2 than 2-h=0=>highlight%28h=2%29
and range of (-infinity,3]=> means k=3 ( so,for x=2 we will have y=3)
so far, your equation is: f%28x%29=a%2Asqrt%28x-2%29+%2B3+
(6,-3)
now use given point point (6,-3) to find a


-3=a%2Asqrt%286-2%29+%2B3+
-3-3=a%2Asqrt%284%29+
-6=a%2A2+
-3=a+
highlight%28a=-3%29+
and, your equation is: f%28x%29=-3%2Asqrt%28x-2%29+%2B3+






Answer by yongweizhen(1) About Me  (Show Source):
You can put this solution on YOUR website!
a small correction
y =a√(x-2)+3
-3=a√(6-2)+3
-6=a√4
a=-3