📚 Topic Summary
The quadratic formula is your go-to tool for solving quadratic equations of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. It provides a straightforward method to find the roots (or solutions) of these equations, even when factoring is difficult or impossible. Mastering this formula is essential for success in Algebra 1 and beyond.
The formula itself is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Remember, the '$\pm$' means you'll have two possible solutions, one with addition and one with subtraction.
🧠 Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. Quadratic Equation |
A. The point where the parabola intersects the y-axis. |
| 2. Root |
B. A solution to a quadratic equation. |
| 3. Parabola |
C. An equation in the form $ax^2 + bx + c = 0$. |
| 4. Vertex |
D. The U-shaped curve representing a quadratic function. |
| 5. Y-intercept |
E. The highest or lowest point on a parabola. |
Write your answers here: 1: ___, 2: ___, 3: ___, 4: ___, 5: ___
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided below:
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. In this formula, $a$, $b$, and $c$ are __________ from the quadratic equation written in __________ form. The expression $b^2 - 4ac$ is known as the __________, which helps determine the number of __________ the equation has.
Words: coefficients, standard, discriminant, solutions
🤔 Part C: Critical Thinking
Explain in your own words why understanding the quadratic formula is important for solving real-world problems. Give an example of a situation where it might be useful.