Answer:
Step-by-step explanation:
Recognize from examining this function h( x ) = ( x + 1 )^2 - 4 that it is a quadratic function whose graph is a parabola that opens up. The vertex is at (h, k): (-1, -4). The axis of symmetry is the vertical line passing through the vertex: x = -1.
To find the y-intercept, let x = 0 and solve for y: h(0) = (0 + 1)^2 - 4 = -3. Thus, the y-intercept is (-3, 0).
To find the x-intercepts, set y = 0 and solve for x: 0 = h(x) = (x + 1)^2 - 4, or
(x + 1)^2 = 4. Taking the square root of both sides, we get x + 1 = ±2, whose roots are x = 1 and x = -3: (1, 0) and (-3, 0).
Graph all of these points and the axis of symmetry. Sketch the parabola that goes through these points.
