From the image you've provided, we have the following components:

• The equation of the parabola is given as $f(x) = ax^2 + bx + c$.
• The graph shows a parabola that opens upwards (concave up), indicating that $a > 0$.

Now, let's analyze the four statements:

1. $a > 0$:

   • Since the parabola opens upwards, the coefficient $a$ is positive.
   • This statement is TRUE.

2. $b > 0$:

   • The value of $b$ controls the horizontal shift of the vertex, but from just the shape of the parabola, it's not possible to directly conclude the sign of $b$. We cannot be sure that $b > 0$.
   • This statement is FALSE.

3. $c > 0$:

   • The constant $c$ represents the y-intercept of the parabola (the value of $f(x)$ when $x = 0$).
   • In this graph, the parabola intersects the y-axis above the origin, so $c > 0$.
   • This statement is TRUE.

4. $b^2 > 4ac$:

   • This is the discriminant of the quadratic equation, which determines the number of real roots.
   • For $b^2 > 4ac$, the equation would have two distinct real roots. However, the graph shows a parabola with one minimum point, suggesting that the discriminant is less than or equal to zero, meaning $b^2 - 4ac \leq 0$.
   • This statement is FALSE.

In summary, the correct answers are:

• $a > 0$: BENAR (TRUE)
• $b > 0$: SALAH (FALSE)
• $c > 0$: BENAR (TRUE)
• $b^2 > 4ac$: SALAH (FALSE)

Would you like more details or clarifications on any of the points?

Here are five related questions to expand on this:

1. What role does $b$ play in shifting the parabola horizontally?
2. How does the discriminant $b^2 - 4ac$ affect the nature of the roots of a quadratic equation?
3. Can you determine the vertex of the parabola using the coefficients $a$, $b$, and $c$?
4. How does the sign of $a$ affect the direction in which the parabola opens?
5. What happens if $b^2 = 4ac$ in terms of the roots of the quadratic equation?

Tip: When analyzing quadratic equations, the discriminant $\Delta = b^2 - 4ac$ is crucial for understanding the number and type of roots.