Given the parabola:
[tex]y=x^2+4x+4[/tex]a = 1
b = 4
c = 4
The x-coordinate of the vertex is found as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-4}{2\cdot1} \\ h=-2 \end{gathered}[/tex]The x-coordinate of the vertex is found as follows:
[tex]\begin{gathered} k=y(h)=h^2+4h+4 \\ k=(-2)^2+4(-2)+4 \\ k=4-8+4 \\ k=0 \end{gathered}[/tex]Then, the vertex is (-2, 0)
The y-intercept is found as follows:
[tex]y_{\text{ int}}=y(0)=0^2+4\cdot0+4=4[/tex]The y-intercept is (0,4)
The vertical line: x = h, in this case x = -2 is the symmetry axis. Then the point
(-4, 4) is on the parabola. With these 3 points, we can plot the function. The graph is:
