Question

find the range of the quadratic function.
f(x) = (x+8)^2 - 7

Answer 1

I think it is (-infinity, -7)

Answer 2

No...

Answer 3

do i factor it out and find the maximum

Answer 4

Put f(x) = y first:

\[y = (x+8)^2 - 7\]

\[(x+8)^2 = y + 7\]

\[x + 8 = \sqrt{y + 7} \implies x = \sqrt{y + 7} - 8\]

Answer 5

What values y cannot take??

Answer 6

Number inside the square root must not be negative..

So:

\[y + 7 \ge 0\]

Can you solve now??

Answer 7

Subtract both the sides by 7 and tell me what do you get??

Answer 8

-7

Answer 9

so is it (-7, infinity)

Answer 10

Yes...

Answer 11

thank you again