The vertex of the graph of a quadratic function is in the second quadrant. The related equation has no real solutions. Which statement is true?

a) The graph opens up.

b) The graph opens down.

c) The y-intercept is 0.

d) The axis of symmetry is x = 0.

Answer: a) The graph opens up.

Step-by-step explanation:

The vertex is the minimum/maximum of a parabola.

We know that the vertex is in the second quadrant (so it is in the quadrant of positive y values and negative x values)

We also know that it has no real roots, so the graph never touches the x-axis, and knowing that the vertex is above the x-axis, then the graph must open upwards.

Then the correct option is:

a) The graph opens up.