Question

Which statements are true about the graph of the function f(x) = 6x – 4 + x2? Check all that apply. The vertex form of the function is f(x) = (x – 2)2 + 2. The vertex of the function is (–3, –13). The axis of symmetry for the function is x = 3. The graph increases over the interval (–3, ). The function does not cross the x-axis.

Answer 1

B and D

Explanation:

Answer 2

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, )