Question

Hi ( :can anyone help me solve this?
Use interval notation to state the range of the quadratic function.

f(x) = -2(x + 1)^2 - 3

Answer 1

lets take it step by step

Answer 2

the smallest \((x+1)^2\) can be is 0, because if you square any non zero number it is positive

Answer 3

therefore the LARGEST \(-2(x+1)^2\) can be is zero, otherwise it is negative (less than zero)

Answer 4

and finally that means the largest \[-2(x+1)^2-3\] can be is \(-3\)

Answer 5

that makes the range all numbers less than or equal to \(-3\) which, in interval notation, is
\[(-\infty, -3]\)

Answer 6

\[(-\infty, -3]\]

Answer 7

Thank you

Answer 8

yw

Answer 9

would please help me with another question?

Answer 10

On which interval is f(x) = (x - 6)2 + 3 decreasing?