To draw the graph of the given written in , 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 graph the function.

- 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 $

$x=2$

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

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

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 the given equation.

$f(x)=-x_{2}+4x+4$

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

$f(2)=-4+4(2)+4$

$f(2)=-4+8+4$

$f(2)=8$

We found the

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

$(2,8).$ ### 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 negative, the parabola will open * downward *. Let's connect the three points with a smooth curve.