SOLUTION: Find the range of the function and write it using interval notation: f(x)=10-(x-2)^2

Algebra ->  Functions -> SOLUTION: Find the range of the function and write it using interval notation: f(x)=10-(x-2)^2      Log On


   

Question 912258: Find the range of the function and write it using interval notation:
f(x)=10-(x-2)^2
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=10-(x-2)^2

f(x)=-1(x-2)^2 + 10

that equation is in the form y = a(x-h)^2 + k where a = -1, h = 2, k = 10

The value of 'a' is negative, so this is a parabola that opens downward. That means it has a peak point.

The peak is at (2, 10) which is the vertex.

Range: y%3C=10

Range in interval notation:

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the range of the function and write it using interval notation:
f(x)=10-(x-2)^2
solve for x in terms of y
y=10-(x-2)^2
(x-2)^2=10-y
x-2=±√(10-y)
x=2±√(10-y)
(10-y)≥0 (radican≥0)
-y≥-10
y≤10
range:(-∞,10]