We are tasked to complete the table for $y = x^2 - 3x - 2$ and find values for $A$, $B$, and $C$ corresponding to specific $x$-values.

The table:

We calculate $y$ for the missing values using the equation:

$y = x^2 - 3x - 2$

Step-by-step Calculations:

1. For $x = -1$ (to find $A$): $y = (-1)^2 - 3(-1) - 2$ $y = 1 + 3 - 2 = 2$ So, $A = 2$.

2. For $x = 0$ (to find $B$): $y = 0^2 - 3(0) - 2$ $y = 0 - 0 - 2 = -2$ So, $B = -2$.

3. For $x = 3$ (to find $C$): $y = 3^2 - 3(3) - 2$ $y = 9 - 9 - 2 = -2$ So, $C = -2$.

Final Table:

Final Answers:

• $A = 2$
• $B = -2$
• $C = -2$

Let me know if you need further explanations or additional examples! 😊

Related Questions:

1. What is the general shape of the graph of $y = x^2 - 3x - 2$?
2. How do you find the vertex of $y = x^2 - 3x - 2$?
3. What are the roots (or $x$-intercepts) of $y = x^2 - 3x - 2$?
4. Can you factorize $x^2 - 3x - 2$?
5. How do you plot this quadratic equation on a graph?

Tip:

The coefficient of $x^2$ in a quadratic equation determines whether the parabola opens up ($a > 0$) or down ($a < 0$).