Question

Given f(x) = x^2 - 10x + 22, what is the range of f?

Answer 1

f(x)=x2-10x+22 domain of f

Answer: all real numbers

Range of F

Answer: y> -3

Answer 2

The range is all the possible y-values.

For a parabola that opens up, it is everything greater than the vertex.

If the vertex is (h,k) then the range is y >= k.

Vertex can be found using completing the square:

`x^2 -10x +22 \\ \\ (x^2 -10x + ((-10)/(2))^2) +22 - ((-10)/(2))^2 \\ \\ (x^2 -10x+25) +22-25 \\ \\ (x-5)^2 - 3`
(h,k) = (5,-3) ------> Range is y >= -3

Vertex may also be found using formula
`h = (-b)/(2a)`
a = 1, b = -10, c = 22

`h = (10)/(2) = 5`

`k = 5^2 - 10(5) +22 \\ \\ k = 25 -50+22 \\ \\ k = -3`
------> Range is y >= -3