This problem involves analyzing the properties of a quadratic function $y = ax^2 + bx + c$ given its graph, and determining which statement about the constants $a$, $b$, and $c$ is correct.

From the image:

• The graph is a parabola that opens upward, indicating that $a > 0$.
• The parabola crosses the $x$-axis at two points, so the discriminant $\Delta = b^2 - 4ac > 0$ (there are two real roots).
• The parabola crosses the $y$-axis above the origin, indicating that $c > 0$.
• $ab$ depends on the relative signs of $a$ and $b$.

We analyze each choice to determine the correct statement:

Key observations:

1. $a > 0$ since the parabola opens upwards.
2. $b$ can be positive or negative (depending on the symmetry of the graph).
3. $c > 0$ since the $y$-intercept is positive.

Options analysis:

• Option A: $ab > 0$ and $a + b + c > 0$.
  $ab > 0$ implies $b > 0$ (as $a > 0$). This holds if $a + b + c > 0$.

• Option B: $ab < 0$ and $a + b + c > 0$.
  Incorrect, as $a > 0$, $ab$ cannot be negative.

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