Question

Graph the function

V(x)=x^2 + 4x +4

Answer 1

To graph the function V(x) = x^2 + 4x + 4, we can first find the vertex of the quadratic function by using the formula for the x-coordinate of the vertex: x = -b/2a.

In this case, a = 1, b = 4. So x = -4/(2*1) = -2.

Now, substitute x = -2 back into the original function to find the y-coordinate of the vertex: V(-2) = (-2)^2 + 4(-2) + 4 = 4 - 8 + 4 = 0.

Therefore, the vertex of the function V(x) = x^2 + 4x + 4 is (-2,0).

Next, we can find the x-intercepts by setting V(x) = 0 and solving for x:

0 = x^2 + 4x + 4
0 = (x + 2)^2

This implies that the x-intercept is x = -2.

Finally, let's plot these points on a graph:

The vertex is at (-2, 0) and the x-intercept is at (-2, 0). The graph is a parabola that opens upwards.

Now, let's plot the graph of the function V(x) = x^2 + 4x + 4:

graph{y = x^2 + 4x + 4 [-10, 10, -10, 10]}