Final answer:
A positive (x-3) suggests that values of x greater than 3 will satisfy the condition. The statement about the graph being concave downward is determined by the leading coefficient of a quadratic function, not solely by the sign of (x-3). The discriminant being greater than zero indicates real and distinct roots but doesn't determine concavity.
The discriminant is greater than zero.
Step-by-step explanation:
If (x-3) is positive, we are looking to understand which statement about a quadratic function or inequality is true. Since (x-3) is positive, this means any value of x greater than 3 will satisfy this condition.
If we consider a quadratic function such as f(x) = ax^2 + bx + c, where a, b, and c are constants, we must look at the sign of the leading coefficient 'a' to determine if the graph is concave up or concave down. A concave downward graph would have a negative leading coefficient.
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 - 4ac. If the discriminant is greater than zero, the quadratic equation will have real and distinct roots. Nevertheless, this information alone is not sufficient to determine the concavity of the quadratic function's graph.
Lastly, the notation for the solution of x provided in the question seems to be unclear or incorrect. Typically, the solution for x in an inequality will be written in interval notation such as (a, b) or [a, b].
The discriminant is greater than zero.