To identify the values of $a$, $b$, and $c$ in the quadratic equation, we first need to rewrite the equation in the standard quadratic form, which is:

$ax^2 + bx + c = 0$

The given equation is:

$18 = -9x + 7x^2$

Rearrange the equation so that all terms are on one side, setting it equal to 0:

$7x^2 - 9x - 18 = 0$

Now, you can identify the coefficients:

• $a = 7$ (coefficient of $x^2$)
• $b = -9$ (coefficient of $x$)
• $c = -18$ (constant term)

So the values are:

• $a = 7$
• $b = -9$
• $c = -18$

Would you like further clarification on any of these values?

Here are 8 related questions:

1. How do you use the quadratic formula once you've identified $a$, $b$, and $c$?
2. What does the discriminant $b^2 - 4ac$ tell you about the solutions of a quadratic equation?
3. Can $a$ in a quadratic equation be zero? Why or why not?
4. How do you determine the vertex of a parabola using the values of $a$ and $b$?
5. What is the significance of the sign of $a$ in a quadratic equation?
6. How can you factor a quadratic equation when $a$, $b$, and $c$ are integers?
7. What are the possible types of solutions for a quadratic equation?
8. How do you solve a quadratic equation by completing the square?

Tip: Always ensure the quadratic equation is in standard form $ax^2 + bx + c = 0$ before identifying $a$, $b$, and $c$ or applying the quadratic formula.