Final Answer:
1) The graph crosses the y-axis at (0,c) is True
2) The graph always crosses the x-axis twice is Not always true.
3) The vertex occurs at the point where x = 2a is False.
4) The parabola opens up when a is a positive value is True.
5) The function has at least one point whose y coordinate is zero is True.
Step-by-step explanation:
The statement that the graph crosses the y-axis at (0,c) is true because when x is zero, the y-value is equal to c, representing the y-intercept.
The statement that the graph always crosses the x-axis twice is not always true. The number of x-intercepts depends on the discriminant (b^2 - 4ac). If the discriminant is positive, there are two real roots; if it's zero, there's one real root; and if it's negative, there are no real roots.
The statement about the vertex occurring at the point where x = 2a is false. The x-coordinate of the vertex is given by -b/2a.
The statement that the parabola opens up when a is a positive value is true. If 'a' is positive, the parabola opens upward, and if 'a' is negative, it opens downward.
The statement about the function having at least one point with a y-coordinate of zero is true. This is because the parabola intersects the x-axis at the x-intercepts, and at these points, the y-coordinate is zero.