Questions: Graph the quadratic function f(x)=(x+2)^2. Give the (a) vertex, (b) axis, (c) domain, and (d) range. (a) The vertex is (Type an ordered pair.)

Solution Steps

The vertex of a quadratic function in the form \( f(x) = (x - h)^2 + k \) is given by the point \((h, k)\). For the function \( f(x) = (x + 2)^2 \), we can rewrite it as \( f(x) = (x - (-2))^2 + 0 \). Therefore, the vertex is \((-2, 0)\).

The axis of symmetry for a quadratic function in the form \( f(x) = (x - h)^2 + k \) is the vertical line \( x = h \). For the function \( f(x) = (x + 2)^2 \), the axis of symmetry is \( x = -2 \).

The domain of any quadratic function is all real numbers, since there are no restrictions on the values that \( x \) can take. Therefore, the domain is \((-\infty, \infty)\).

Final Answer