Question

what does a graph look like that is y=x^2+4x+4 with a repeated root of x=-2
opens downward
veterx to right of xaxis
touches x-axis once

Answer 1

Your equation factors to (x + 2)^2, so it is a parabola with a repeated root at x = −2. Correct properties:

- y = x^2 + 4x + 4 = (x + 2)^2
- Vertex: (−2, 0)
- Repeated root: x = −2 (the parabola touches the x‑axis once at x = −2)
- Opens upward (coefficient of x^2 is +1), so the vertex is a minimum point on the x‑axis.

Your listed items “opens downward” and “vertex to right of x‑axis” conflict with the equation. If you intended a parabola that opens downward and still touches the x‑axis once at x = −2, use y = −(x + 2)^2 (vertex still at (−2, 0), but it would be a maximum). If you meant the vertex to the right of the y‑axis, the root would have to be positive (for example (x − 2)^2 touches at x = 2).