Question

This is the graph of $y = {x}^{2} - 2x - 8$I need the range of this function

Answer 1

Answer:

Range = [-9, ∞)

Explanation:

The given equation is:

$y=x^2-2x-8$

Compare the equation with:

$y=ax^2+bx+c$

a = 1, b = -2, c = -8

f(-b/2a) is the minimum value of the range (y)

First find -b/2a

-b/2a = -(-2)/2(1)

-b/2a = 2/2

-b/2a = 1

f(-b/2a) = f(1)

$\begin{gathered} f(1)=1^2-2(1)-8 \\ \\ f(1)=1-2-8 \\ \\ f(1)\text{ = -9} \end{gathered}$

Therefore, the range of the function is all real numbers greater than or equal to -9

Range = [-9, ∞)