Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . G(x)= -x²+4x+5

The correct answer is: ( 2 , 9 )

This quadratic function is in standard form, f(x)=ax²+bx+c.
For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
In g(x)= -x²+4x+5, a= -1, b=4, and c=5. So, the equation for the axis of symmetry is given by
x = −(4)/2(-1)
x = - 4/-2
x = 2
The equation of the axis of symmetry for g(x)=-x²+4x+5 is x = 2.
The x coordinate of the vertex is the same:
h = 2
The y coordinate of the vertex is :
k = g(h)
k = -(h)² + 4(h) + 5
k = -(2)² + 4(2) + 5
k = -4 + 8 + 5
k = 9
Therefore, the vertex is (2 , 9)
For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.
y = -(0)² + 4(0) + 5
y = 0 + 0 + 5
y = 5
Therefore, Axis of symmetry is x = 2
Vertex is ( 2 , 9 )
Y- intercept is 5.