# How do you find the domain and range of f(x) = (x + 8)^2 - 7?

Jan 7, 2018

Inspect using the formula $y = a {\left(x - h\right)}^{2} + k$

#### Explanation:

From the equation given $f \left(x\right) = {\left(x + 8\right)}^{2} - 7$ we can see that:

h = -8
k = -7

From the original equation $y = {x}^{2}$, if h is negative the graph the will shift left or negative x and if k is negative the graph will shift down or negative y.

graph{(x+8)^2-7 [-27.05, 12.95, -8.72, 11.28]}

Since x will keep increasing to infinity regardless of any x-axis transformations the domain will be the same as $y = {x}^{2}$

Domain: All real numbers

However, since a minimum applies to the range, if the graph shifts in the y-axis the range will be different from $y = {x}^{2}$

Range: y ≥ -7