Question

Find the domain and range of x^2-6x+14-y=0

Answer 1

I would write this as
y= x^2-6x+14

the domain are the "legal" x values
if you don't divide by 0 or take the root of a negative number, all x values are legal
so you should know what the domain is, right?

Answer 2

I guess just all real numbers

Answer 3

yes (-inf, +inf)

Answer 4

for the range, you have to find the min and max of the y values.

Notice that this is a parabola. I would find the vertex, and then the min y value.
the max y value is ??

Answer 5

the max y value? infinity right?

Answer 6

yes y goes to +inf

for polynomials you can just focus on the highest degree x^2 here and ask what happens when x is +(very big number) or -(very big number). you get a +(very big number) which we call +infinity
so the range is

[ ?, +inf)

Answer 7

for
ax^2 + bx +c
the vertex is at x=-b/(2a)
use that x to find the min y value

Answer 8

the vertex is (3, 5), so y is greater than or equal to 5.

i was absent during this lesson, and the class apparently completed the square, to get (x-3)^2=y-5, and then got the answer. how do you get the vertex from there?

Answer 9

the equation of a parabola in vertex form is
y = a (x-h)^2 +k
the vertex is (h,k) (hence the name, "vertex form"

in this case
y = (x-3)^2 + 5
and you read off (3,5)

Answer 10

you can see when x is 3 you get (3-3)^2 or 0 and 0+5 is 5
if x is something other than 3 you get a number and when you square it, it is positive
so you add something to 5, and y is bigger. This is a long way to say x=3 must give the min value of y

Answer 11

your answer is
domain (-inf, +inf)
range [5, +inf)
(you use square bracket to show the range includes 5)
you use parens for the infinity (because infinity isn't a number)

Answer 12

thanks!