Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . H(x)= -3x²+7x+1

The correct answer is: ( 1.167 , 5.083 )

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 H(x)= -3x²+7x+1, a= -3, b=7, and c=1. So, the equation for the axis of symmetry is given by
x = −(7)/2(-3)
x = - 7/-6
x = 7/6
The equation of the axis of symmetry for H(x)= -3x²+7x+1 is x = 7/6.
The x coordinate of the vertex is the same:
h = 7/6
The y coordinate of the vertex is :
k = H(h)
k = -3(h)² + 7(h) + 1
k = -3(7/6)² + 7(7/6) + 1
k = -(49/12) + (49/6) + 1
k = 5.083
Therefore, the vertex is (1.167 , 5.083)
For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.
y = -3(0)² + 7(0) + 1
y = 0 + 0 + 1
y = 1
Therefore, Axis of symmetry is x = 7/6
Vertex is ( 1.167 , 5.083 )
Y- intercept is 1.