Question

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

Answer 1

Factor the quadratic: y = x^2 + 4x + 4 = (x + 2)^2.

- It is a parabola opening upward (coefficient of x^2 is +1), so "opens downward" is false.
- The vertex is at (-2, 0) (axis of symmetry x = -2). The vertex lies on the x-axis and is left of the y-axis, so it is not "to the right" of the y-axis. If by "to right of x-axis" you meant something else, clarify — the vertex is on the x-axis (y = 0).
- Because the factor is a perfect square, the parabola has a repeated root at x = −2 and therefore touches the x-axis exactly once (tangent there) — that statement is true.

Quick sketch (rough):

y
^
5| *
4| * (0,4)
3|
2|
1|
0|_____*________> x
-2

Vertex at (-2,0), minimum value 0.