Based on the image provided, here’s how to analyze the problem:

You are given the quadratic equation $f(x) = ax^2 + bx + c$ representing a parabola. The parabola opens upwards, as shown in the diagram. You are asked to determine whether the statements about the parameters $a$, $b$, $c$, and the discriminant $b^2 - 4ac$ are correct or not.

Analysis:

1. $a > 0$
   Since the parabola opens upwards, the coefficient of $x^2$ (which is $a$) must be positive.
   Conclusion: This statement is correct ("BENAR").

2. $b > 0$
   From the image, we don't have direct information about $b$ (the coefficient of $x$), but the parabola seems to be symmetric around the vertical axis, implying $b = 0$, not $b > 0$.
   Conclusion: This statement is incorrect ("SALAH").

3. $c > 0$
   The vertex of the parabola is below the x-axis, indicating that $c$, the y-intercept, is positive.
   Conclusion: This statement is correct ("BENAR").

4. $b^2 > 4ac$
   The discriminant $\Delta = b^2 - 4ac$ determines the nature of the roots. Since the parabola does not touch or cross the x-axis, the roots are imaginary, meaning $\Delta < 0$, or $b^2 < 4ac$.
   Conclusion: This statement is incorrect ("SALAH").

Final Answers:

• $a > 0$: BENAR
• $b > 0$: SALAH
• $c > 0$: BENAR
• $b^2 > 4ac$: SALAH

Would you like further details on any part of the explanation?

Here are some related questions to deepen your understanding:

1. What is the significance of the discriminant $b^2 - 4ac$ in quadratic equations?
2. How does the value of $a$ affect the direction of a parabola?
3. What does the term $c$ represent in the quadratic equation?
4. Can a parabola open downwards? If yes, what condition must $a$ satisfy?
5. How can you determine the vertex of a parabola from its equation?

Tip: The discriminant helps in determining whether a parabola intersects the x-axis (real roots), touches it (one root), or stays above or below (complex roots).