Assume both statements are true, and consider these two equations:

Case 1: 

The -intercept can be proven to be  by substituting 0 for :

We show that the graph intersects the line of equation  twice by substituting 3 for :

The points of intersection are .

To find the -intercept(s), if any exist, substitute 0 for :

This has no real solutions, so the parabola has no -intercepts.

Case 2: 

The -intercept be proved to be  by substituting 0 for :

We show that the graph intersects the line of equation  twice by substituting 3 for :

We examine the discriminant:

The discriminant is positive, so there are two real solutions, meaning that there are two points of intersection. 

To find the -intercept(s), if any exist, substitute 0 for :

We examine this discriminant:

The discriminant is positive, so there are two real solutions, meaning that there are two -intercepts.

Two parabolas have been identified fitting the main condition and those of both statements, but one has no -intercept and one has two. The two statements together provide insufficient information.

The line of symmetry of a vertical parabola is the vertical line passing through the vertex. Each statement alone gives only one point on the graph, neither of which is the vertex, so neither statement alone gives sufficient information.

Now assume both statements to be true. Statement 1 gives one -intercept, ; Statement 2 states that the graph passes through the origin, so it is not only the -intercept, it is also the other -intercept. The -coordinate of the vertex is the arithmetic mean of those of the two -intercepts, so that value is

Only the -coordinate of the vertex is needed to answer the question - we can immediately deduce that the line of symmetry is .

The parabola is concave upward if and only if , and concave downward if and only if . Therefore, we need to know the sign of  to answer the question. We show that the two statements together provide insufficient information by examining two equations.

Case 1: 

; we check the values of the expressions in both statements:

The conditions of both statements are satisfied; since , the parabola that graphs this function is concave upward.

Case 2: 

; we check the values of the expressions in both statements:

The conditions of both statements are satisfied; since , the parabola that graphs this function is concave downward.

The two statements together give the vertex of the parabola, but no clue is given as to the orientation of the parabola - horizontal, vertical, or otherwise. Without that information, or any way to find it, the line of symmetry cannot be determined.

Assume both statements are true.

The parabola is concave upward if and only if , and concave downward if and only if . Therefore, we need to know the sign of  to answer the question. We show that the two statements together provide insufficient information by examining two equations.

Case 1: 

If we substitute 0 for ,  is easily seen to be equal to 6, so the -intercept is . Also:

Case 2: 

If we substitute 0 for ,  is easily seen to be equal to 6, so the -intercept is . Also:

Each equation satisfies the conditions of both statements, but  is positive in one equation and negative in the other.  can assume either sign, so the question of the parabola's concavity is unresolved.