Answer: See the graph attached.
Explanation:
The standard form of a quadratic function is:
![f(x)=a(x-h)+k]()
Where (h,k) is the vertex of the parabola.
If
![a]()
is negative, then the parabola opens down.
Then, for the function:
![f(x)=-(x-2)^2+4]()
You can identify:
![h=2\\k=4]()
Then the vertex of the parabola is at (2,4)
Note that
![a=-1]()
, therefore the parabola opens down.
Find the intersection with the x-axis. Substitute
![f(x)=0]()
and solve for x:
![0=-(x-2)^2+4\\0=x^2-4x\\0=x(x-4)\\\\x_1=0\\x_2=4]()
Knowing that the vertex is at (2,4), the parabola opens down and it intersects the x-axis at x=0 and x=4, you can graph the function, as you observe in the figure attached.