Identifying Characteristics of Quadratic Functions

Let us start by listing the characteristics of the quadratic function in the graph.

• The curve has an absolute minimum.
• The curve intersects the positive part of the $y$-axis.

With this information, we can exclude some functions.

Minimum point

The second degree curve has an absolute minimum which means that the coefficient in front of $x^2$-term must be positive. Therefore, we can exclude B.

The point of intersection with the $y$-axis

Because the curve cuts the positive part of the $y$-axis the constant term also has to be positive, which means that you can exclude the function C which has the constant $\text{-}6.$

Conclusion

The only function left is function A.