Question

What is the domain and range of the quadratic equation y = -3(x - 10)^2 + 5?

Answer 1

I don't know what range means

Answer 2

what is the vertex of this parabola

Answer 3

-3?

Answer 4

in general

y = a(x-h)^2 + k

has the vertex (h,k)

Answer 5

so its (-10,5)?

Answer 6

closer

Answer 7

it's actually (10, 5)

Answer 8

since h = 10 and k = 5

Answer 9

the y coordinate of this vertex is y = 5

this is either the min or max that y can be

do you know which it is (min or max)?

Answer 10

I have no idea

Answer 11

ill say min

Answer 12

the leading coefficient is a = -3

Answer 13

so this means that the parabola opens downward

so this means there is a maximum, which is the vertex

Answer 14

so y = 5 is the largest possible y value on the graph

Answer 15

how does that help us find the range?

Answer 16

because y=5 is the largest possible y value on the graph

Answer 17

yes how can you use that to find the range

Answer 18

and what is the range

Answer 19

idk :'(

Answer 20

the range is the set of all possible output values of a function, ie the set of all possible y values

Answer 21

so if you know the max y value you can use this to find the range

Answer 22

so the range is 5?

Answer 23

not just 5, but it includes other values as well

Answer 24

greater than?

Answer 25

what's another value that's in the range?

Answer 26

1)Domain: All Real Numbers
Range: y alt= 5

2)
Domain: All Real Numbers
Range: y alt= 5

Answer 27

I have two answers to choose, which one would it be?

Answer 28

number 1 is less than 5, and number 2 is greater than 5

Answer 29

what's another y value that is in the range

Answer 30

10

Answer 31

remember y = 5 is the largest possible y value (the parabola opens downward, so it peaks)

Answer 32

I say greater than 5

Answer 33

here's what the parabola looks like

Answer 34

the peak is here (so the vertex is here)