📚 Topic Summary
The zeros of a quadratic function are the $x$-values where the function equals zero. Graphically, these are the points where the parabola intersects the $x$-axis. Finding these zeros is crucial for understanding the behavior of quadratic equations and solving real-world problems. We can determine the zeros using factoring, the quadratic formula, or completing the square. Let’s practice!
🧠 Part A: Vocabulary
Match the following terms with their correct definitions:
| Term |
Definition |
| 1. Quadratic Function |
a. The highest or lowest point on the parabola. |
| 2. Zero |
b. A U-shaped curve representing a quadratic function. |
| 3. Parabola |
c. A value of $x$ that makes the function equal to zero. |
| 4. Vertex |
d. An equation of the form $f(x) = ax^2 + bx + c$, where $a \neq 0$. |
| 5. Discriminant |
e. The expression $b^2 - 4ac$ used to determine the nature of roots. |
✍️ Part B: Fill in the Blanks
A quadratic function can be written in the form $f(x) = ax^2 + bx + c$. The zeros of the function are also known as the _________ of the equation. The graph of a quadratic function is a _________, which opens upward if $a > 0$ and downward if $a < 0$. The _________ formula can be used to find the zeros even when factoring is not possible. The number of real zeros can be determined using the _________.
🤔 Part C: Critical Thinking
Explain in your own words how the discriminant of a quadratic equation can tell you about the number and type of zeros the function has.