For the graph of the function below, identify the axis of symmetry, vertex and formula for the function

The correct set of answers is D. 

For the line of symmetry, this you can find by looking at the graph. Each graph of a quadratic will have a line of symmetry that goes right through it's highest or lowest point (also known at the vertex). 

Which brings us to finding the vertex. The vertex is the highest or lowest point in a quadratic. We obviously can't see the lowest point because it keeps going down. So in this case, we use the highest point. This would be (0.5, -.75)

Finding the equation of the graph is the trickiest. However, you can use an equation that helps to find the vertex as a good way to check. The x value of the vertex is -b/2a in which a is the number attached to x^2 and b is the number attached to x. If we test the equation in answer D, a would be equal to -1 and b would be equal to 1. 

x value = -b/2a
x value = -(-1)/2(1)
x value = 1/2
x value = 0.5

Since this is the only equation that will give you that value, then we know it must be the correct one.