Find the vertex of the given function. \( f(x)=|x+1|-7 \) The vertex is at \( (\square \) DONE

The function \( f(x) = |x + 1| - 7 \) is in the standard form of absolute value functions, where the vertex can be identified from the expression inside the absolute value. Here, \( x + 1 = 0 \) gives us \( x = -1 \). To find the y-coordinate of the vertex, substitute \( x = -1 \) back into the function: \( f(-1) = |0| - 7 = -7 \). Thus, the vertex is at \( (-1, -7) \). If you're plotting the function, you'll see that the graph forms a "V" shape, with the vertex being the lowest point on the graph since this opens upwards. The x-coordinate of the vertex corresponds to the point where the expression inside the absolute value equals zero, leading to that minimum output value at the vertex.