Answer:
a < 0
The vertex is (1,2)
Explanation:
Looking at the graph
we have a vertical parabola open downward
The leading coefficient is negative
The vertex is a maximum
The vertex is the point (1,2)
The axis of symmetry is equal to the x-coordinate of the vertex, so the axis of symmetry is x=1
The y-intercept is the point (0,1)
The function has two real solutions (zeros of the function) one positive and one negative
The positive zero of the function is greater than 2
The negative zero of the function is greater than -1
Verify each statement
case 1) a < 0
The statement is true
Because the parabola open downward
case 2) The vertex is (1,2)
The statement is true
The vertex in this problem is the maximum of the function
case 3) The axis of symmetry is y =2
The statement is false
Because the axis of symmetry is x=1
case 4) x = 2 is a zero of the function
The statement is false
Because the positive zero of the function is greater than 2
case 5) (1,2) is a minimum
The statement is false
Because the vertex in this problem is a maximum