Question

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Answer 1

domain = R
range = ]-infinite, 8]

Answer 2

I'm confused about what you put for the range? What is the range and domain, like, what IS it literally in the equation?

Answer 3

domain is ALWAYS R = all numbers (in your case)
range is the maximum to - infinite
or the minimum to + infinite

Answer 4

Oh! Okay. Well thanks!

Answer 5

I was thinking the domain and range would be actual number from the equation or something.

Answer 6

do you know how to find the range?

Answer 7

Nope.

Answer 8

since you have a parabola that opens down, it has a maximum value
that is the second coordinate of the vertex
the first coordinate of the vertex you find by \(x=-\frac{b}{2a}\) the second coordinate you find by replacement

Answer 9

you have
\[y=-x^2 + 12x - 28\] so in this case \(a=-1,b=12\) and \(-\frac{b}{2a}=-\frac{12}{2\times (-1)}=6\)

Answer 10

and 6 is what? the range? AHH, im so confused!

Answer 11

replace x by 6 and get
\[y=-6^2+12\times 6-28\]
\[y=-36+72-28\]
\[y=8\]

Answer 12

ok lets go slow

Answer 13

the range is the possible y values, not x values

Answer 14

but in order to find the largest possible y value, you first need to find the x value that gives it

Answer 15

as i wrote, you find the x value that gives the largest y by finding \(-\frac{b}{2a}\)
now that is an x value, not a y value, so you find the y by replacing x by that number

Answer 16

so your parabola
\[y=-x^2+12x-28\] will never be bigger than 8, but it can be as small as you like.
so the range is
\((-\infty, 8)\)