Final answer:
The function f(x) = 3x^2 + 7x - 20 is a quadratic function with a leading coefficient of 3. It is not a linear function and has a minimum point. It has two real roots.
Step-by-step explanation:
The function f(x) = 3x2 + 7x - 20 is a quadratic function because it has a squared term (x2) and no higher degree terms. Therefore, the statement A is true.
A linear function has a degree of 1, meaning it is in the form y = mx + b where m is the slope and b is the y-intercept. Since the given function is a quadratic function, it is not a linear function. Therefore, statement B is false.
The vertex of a quadratic function occurs at the minimum or maximum point. In this case, the leading coefficient of 3 is positive, indicating a minimum point. Therefore, statement C is true.
A quadratic function can have zero, one, or two real roots (x-intercepts). To find the roots, you can set the function equal to zero and solve for x. In this case, the function 3x2 + 7x - 20 = 0 can be factored as (x - 2)(3x + 10) = 0. Therefore, the function has two real roots: x = 2 and x = -10/3. Therefore, statement D is true.