Respuesta :
[tex]f(x)=-x^2+5[/tex]
the function represents a parabola, the equation of a parabola is
[tex]y=ax^2+bx+c[/tex]In our case
a=-1
b=0
c= 5
the x coordinate of a parabola can be found with the next formula
[tex]x=-\frac{b}{2a}[/tex]we substitute the values
[tex]x=-\frac{0}{2(-1)}=0[/tex]then we substitute the value of x in the equation in order to find the y- coordinate
[tex]\begin{gathered} f(x=0)=0+5 \\ f(x=0)=5 \end{gathered}[/tex]the vertex is (0,5), as we can see the axis of symmetry of the function is the y-axis
the domain is the set of all possible values that can have x, in this case, the domain is
[tex](-\infty,\infty)[/tex]in other words all the real numbers
the range is the set of all possible values that can have f(x)
assuming f(x)=y, we need to isolate x in order to know the range
[tex]x=\sqrt[]{-y+5}[/tex]we can't have negative values in the square root so the range is
[tex](-\infty,5\rbrack[/tex]