How to find out the quadrant in which the vertex of this equation will lie

Question

Given a quadratic equation $ ax^2 + bx + c = 0 $, whose roots are real and unequal; where $ a,b,c \ \in \mathbb R^+ $ then the vertex of graph will lie in which quadrant?

Answer 1

Hint. Note that the inequalities $a,b,c>0$ imply that the two real roots are both negative (because $ax^2 + bx + c>0$ for $x\geq 0$), and the parabola is $y=ax^2 + bx + c = 0$ is opening to the top.

Answer 2

Hint 1: Since $a>0$, what is the shape of the graph? (Is it U-shaped or an inverted U?)

Hint 2: Since the roots are real and unequal, the graph intersects the $x$-axis at two distinct points.

Hint 3: Show that the roots are negative.