Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S3-SA5-0307
What is a Turning Point of a Graph?
Grade Level:
Class 9
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
A turning point of a graph is a point where the graph changes its direction. It's where the graph stops going up and starts going down, or stops going down and starts going up. These points represent maximum or minimum values.
Simple Example
Quick Example
Imagine the number of likes on your Instagram post over a few hours. It might increase quickly, reach a peak (a turning point!), and then slowly stop increasing or even decrease if some people unlike it. The point where the likes were highest is a turning point.
Worked Example
Step-by-Step
Let's look at the daily temperature in a city. Suppose the temperature started at 20 degrees Celsius in the morning, went up to 35 degrees at noon, and then came down to 25 degrees by evening.
Step 1: Identify the starting trend. The temperature went from 20 to 35, which is an increase.
---
Step 2: Identify the next trend. The temperature went from 35 to 25, which is a decrease.
---
Step 3: Locate where the trend changed. The temperature stopped increasing and started decreasing at 35 degrees.
---
Step 4: Conclude the turning point. The turning point is when the temperature was 35 degrees Celsius, as it was the highest point before it started falling.
Answer: The turning point for temperature in this example is 35 degrees Celsius (at noon).
Why It Matters
Understanding turning points helps scientists predict the peak of a viral spread or economists find the maximum profit for a business. Data scientists use this to find optimal solutions, and engineers use it to design efficient systems, leading to innovations in AI/ML and even space technology like ISRO missions.
Common Mistakes
MISTAKE: Thinking any point where the graph bends is a turning point. | CORRECTION: A turning point specifically means the graph changes from increasing to decreasing, or vice-versa. A simple curve or slight wobble isn't always a turning point.
MISTAKE: Only looking for the highest point as a turning point. | CORRECTION: Turning points can be both maximum points (highest) or minimum points (lowest) where the graph changes direction.
MISTAKE: Confusing a turning point with the start or end point of a graph. | CORRECTION: A turning point is an intermediate point where the direction of the curve changes, not necessarily the beginning or end of the entire graph.
Practice Questions
Try It Yourself
QUESTION: A graph shows the height of a cricket ball hit by Virat Kohli. It goes up to 50 meters and then comes down. What is the turning point in terms of height? | ANSWER: 50 meters
QUESTION: A graph shows the price of a mobile phone over a year. It dropped from ₹15,000 to ₹10,000, then increased to ₹12,000, and finally dropped to ₹9,000. Identify all turning points. | ANSWER: ₹10,000 (minimum) and ₹12,000 (maximum)
QUESTION: Imagine a graph of your study focus over a day. You start with 60% focus, it drops to 30% after lunch, then rises to 80% in the evening, and finally drops to 20% before sleep. What are the turning points and what do they represent? | ANSWER: 30% (minimum focus after lunch) and 80% (maximum focus in the evening). They represent points where your focus changed from decreasing to increasing, or increasing to decreasing.
MCQ
Quick Quiz
Which of the following best describes a turning point on a graph?
Any point where the graph crosses the x-axis
A point where the graph changes from going up to going down, or vice versa
The starting point of the graph
The point where the graph is completely flat
The Correct Answer Is:
B
A turning point is specifically where the graph's direction of movement changes, from increasing to decreasing or decreasing to increasing. It's not just any bend, or the start/end, or where it's flat.
Real World Connection
In the Real World
In the stock market, analysts use turning points to predict when a stock's price might peak or bottom out, helping investors decide when to buy or sell. For example, a stock tracking app might highlight a turning point to show when a share reached its highest value before falling, or its lowest before rising again.
Key Vocabulary
Key Terms
MAXIMUM: The highest point a graph reaches before turning. | MINIMUM: The lowest point a graph reaches before turning. | TREND: The general direction or pattern of change in a graph. | DIRECTION CHANGE: When a graph stops moving up and starts moving down, or vice versa.
What's Next
What to Learn Next
Great job understanding turning points! Next, you can explore 'Slope of a Line' and 'Gradients'. These concepts will help you understand how steeply a graph is rising or falling, and how to mathematically find these turning points in more complex graphs.
