We want to solve the given by . Let's begin by writing the terms on the left-hand side.
$x_{2}+4x=-4⇔x_{2}+4x+4=0 $
To solve the equation, we will graph the represented by the left-hand side of the above equation. To draw the graph, we must start by identifying the values of $a,$ $b,$ and $c.$
$y=x_{2}+4x+4⇔y=1x_{2}+4x+4 $
We can see that $a=1,$ $b=4,$ and $c=4.$ Now, we will follow four steps to .

- Find the .
- Calculate the .
- Identify the and its across the axis of symmetry.
- Connect the points with a .

### Finding the Axis of Symmetry

The axis of symmetry is a with equation

$x=-2ab .$ Since we already know the values of

$a$ and

$b,$ we can substitute them into the formula.

$x=-2ab $

$x=-2(1)4 $

$x=-24 $

$x=-2$

The axis of symmetry of the parabola is the vertical line with equation

$x=-2.$ ### Calculating the Vertex

To calculate the vertex, we need to think of

$y$ as a function of

$x,$ $y=f(x).$ We can write the expression for the vertex by stating the

$x-$ and

$y-$coordinates in terms of

$a$ and

$b.$
$Vertex:(-2ab ,f(-2ab )) $
Note that the formula for the

$x-$coordinate is the same as the formula for the axis of symmetry, which is

$x=-2.$ Thus, the

$x-$coordinate of the vertex is also

$-2.$ To find the

$y-$coordinate, we need to substitute

$-2$ for

$x$ in our function.

$y=x_{2}+4x+4$

$y=(-2)_{2}+4(-2)+4$

$y=0$

We found the

$y-$coordinate, and now we know that the vertex is

$(-2,0).$ ### Identifying the $y-$intercept and its Reflection

The $y-$intercept of the graph of a quadratic function written in standard form is given by the value of $c.$ Thus, the point where our graph intercepts the $y-$axis is $(0,4).$ Let's plot this point and its reflection across the axis of symmetry.

### Connecting the Points

We can now draw the graph of the function. Since $a=1,$ which is positive, the parabola will open *upward*. Let's connect the three points with a smooth curve.

The of the graph are the solutions to the given equation. By looking at the graph, we can state the values for the $x-$intercepts. Notice that the vertex of the parabola is the only $x-$intercept. Therefore, there is only one solution, which is $x=-2.$