dentifying the values a, b, and c is the first step in using the quadratic formula to find solution(s) to a quadratic equation.

What are the values a, b, and c in the following quadratic equation?

18 = −9x + 7x2


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.

Understand how to identify the values of a, b, and c in a quadratic equation with a detailed step-by-step guide. This problem involves rearranging an equation into standard quadratic form, identifying coefficients, and applying the quadratic formula. Suitable for Grades 7-9 students.

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