It looks like you've uploaded a worksheet titled
"Identifying Zeros" that contains multiple graphs of functions, and the task is to identify the
zeros (also known as
roots or
x-intercepts) of each function.
Since I can't view images directly, I'll guide you through how to solve this type of problem and explain the process step by step. If you can describe the graphs or provide details about them (e.g., coordinates where the graph crosses the x-axis), I can help you identify the zeros.
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🔍 What Are Zeros of a Function?
The
zeros of a function are the
x-values where the graph crosses or touches the
x-axis (i.e., where $ f(x) = 0 $).
To find the zeros:
1. Look at the graph.
2. Identify all points where the graph intersects the
x-axis (where $ y = 0 $).
3. Write down the
x-coordinates of those points.
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📊 Example Walkthrough
Suppose one of the graphs shows a parabola crossing the x-axis at $ x = -2 $ and $ x = 3 $. Then:
- The
zeros are: $ x = -2 $ and $ x = 3 $
- You would write:
Zeros: $ x = -2, 3 $
If the graph just touches the x-axis at one point (like a vertex touching the axis), that’s still a zero — it might be a
double root.
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✔ Steps to Solve Each Problem on the Worksheet
For each graph labeled (a) through (h):
1.
Locate the x-intercepts (points where the graph crosses the x-axis).
2.
Read the x-values at those points.
3.
List the zeros in ascending order.
> Note: Some graphs may have
no real zeros (e.g., a parabola above the x-axis). In that case, write "No real zeros."
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🧩 Common Graph Types & Their Zeros
| Graph Type | How to Find Zeros |
|-----------|-------------------|
| Parabola (quadratic) | Crosses x-axis at 0, 1, or 2 points |
| Cubic | Can cross x-axis up to 3 times |
| Absolute Value | Usually has 1 or 2 zeros |
| Rational/Other | Check where graph touches/crosses x-axis |
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💡 Tips
- If the graph
touches the x-axis but doesn’t cross (e.g., a vertex), it's still a zero (but possibly a repeated root).
- If the graph
crosses the x-axis, it changes sign — this is a
simple zero.
- Always check if the graph passes through the origin ($ x = 0 $) — that’s a zero too.
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📝 Final Answer Format
For each graph, your answer should look like:
(a) Zeros: $ x = -3, 1 $
(b) Zeros: $ x = -1, 0, 2 $
(c) Zeros: $ x = -2 $ (double root)
(d) No real zeros
...
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If you can describe the graphs (e.g., "Graph (a) is a parabola opening upward with x-intercepts at -2 and 4"), I can give you the exact answers for each.
Let me know!
Parent Tip: Review the logic above to help your child master the concept of algebra 2 quadratic functions worksheet.
