The equation given in the image is:

$f(x) = -3x^2 + 5x - 2$

We are tasked with determining the dependent value $f(x)$ corresponding to an independent variable $x$ chosen from the set { -3, -2, -1, 0, 1 }.

To find the corresponding dependent value for each $x$, we substitute the values of $x$ into the equation and calculate $f(x)$.

For $x = -3$:

$f(-3) = -3(-3)^2 + 5(-3) - 2 = -3(9) - 15 - 2 = -27 - 15 - 2 = -44$

For $x = -2$:

$f(-2) = -3(-2)^2 + 5(-2) - 2 = -3(4) - 10 - 2 = -12 - 10 - 2 = -24$

For $x = -1$:

$f(-1) = -3(-1)^2 + 5(-1) - 2 = -3(1) - 5 - 2 = -3 - 5 - 2 = -10$

For $x = 0$:

$f(0) = -3(0)^2 + 5(0) - 2 = 0 + 0 - 2 = -2$

For $x = 1$:

$f(1) = -3(1)^2 + 5(1) - 2 = -3(1) + 5 - 2 = -3 + 5 - 2 = 0$

Now, we match the values from the set { -3, -2, -1, 0, 1 } to the dependent values:

• For $x = 0$, the corresponding $f(x) = -2$.

Thus, the correct answer is -2.

Would you like further details or clarification on this problem?

Additional questions:

1. How can you determine the maximum or minimum value of a quadratic function?
2. What is the general form of a quadratic equation and how is it derived?
3. How do the coefficients in the quadratic equation affect its graph?
4. How can we graph the quadratic equation $f(x) = -3x^2 + 5x - 2$?
5. How does the value of the discriminant affect the nature of the roots in a quadratic equation?

Tip: When dealing with quadratic functions, remember that the vertex represents the highest or lowest point depending on the sign of the leading coefficient.