we have that
f(x) = 6x – 4 + x²
Let
y=f(x)
y = 6x – 4 + x²
Find the equation of the vertical parabola in vertex form
y+4= x² +6x
y+4+9= (x² +6x+9)
y+13= (x+3)²
the vertex is the point (-3,-13)
using a graph tool
see the attached figure
case 1) The vertex form of the function is f(x) = (x – 2)² + 2
Is not correct
The vertex form of the function is f(x) = (x +3)²-13
case 2) The vertex of the function is (–3, –13)
Is correct
case 3) The axis of symmetry for the function is x = 3
Is not correct. The axis of symmetry is x=-3
case 4) The graph increases over the interval (–3, )
Is correct (see the attached picture)
case 5)The function does not cross the x-axis
Is not correct (see the attached picture)
therefore
the answer is
The vertex of the function is (–3, –13)
The graph increases over the interval (–3, )
