Reading and Analyzing Graphs

In this graph, we similarly notice the title, “Quarterly Sales, Employee B”. The horizontal axes labels are Q1 2020, Q2 2020, etc. It appears Q1 is the first quarter, Q2 is the second quarter, and so on. The vertical axes labels are dollars.

The graph is showing the quarterly sales for a different  employee (B). This employee’s sales were approximately $1,500 in the first quarter of 2020. Each quarter this employee’s sales decrease through the fourth quarter of 2021 when their sales were approximately $700.

Note: When you read the graph left-to-right and the graph line goes down, we say the graph is decreasing.

In this graph, we first notice the title, “Gallons of Fuel in a Boeing 747”. The horizontal axes label is Hours of Flying. The vertical axes is Fuel, in gallons. The horizontal axis ends at 11 hours. We can assume this graph is showing us the amount of fuel a Boeing 747 airplane burns in one 11 hour flight.

After one hour of flight, the airplane has a little over 35,000 gallons of fuel. Because the line is going down as we read it left-to-right, we say the graph is decreasing. In addition, because the graph appears to be a perfectly straight line, this graph is called a linear graph.

Note: The graph is not realistic to model a true flight of a 747 airplane. More fuel is needed to take off and reach flying altitude than to flying at a constant rate for the duration of the flight. What might a more realistic graph look like?

Here we notice the title, “GPA vs. Hours Worked at Paid Job”. The horizontal axes labels are Hours Per Week Worked in Paid Job. The vertical axes is College GPA.

This graph appears to tell the story of students who attend college and also work in a paid job. Their corresponding GPA’s (Grade Point Averages) are graphed. The GPA increases as students work from 10 to 25 hours, and decreases as the hours go from 25 to 40 hours. The maximum GPA can be thought of as the height (in the vertical direction) at the “top of the peak.” The graph suggests that GPA increases for students as they work in a paid job, up to about 25 hours. Then GPA goes down when students work more than 25 hours.

This shape of a graph is called a parabolic graph. Parabolic graphs come from quadratic functions. See below for more on parabolic graphs.

Parabolic graphs can open “upwards” or “downwards”. They can open wide or narrow. On parabolas that open downward, the highest vertical height of is called the maximum.  On parabolas that open upward, the lowest vertical height of is called the minimum.

Examples of quadratic equations (those that create parabolas) include:

Duckweed is a plant that grows in ponds and covers the surface of the pond. This graph is modeling the surface area of the pond covered by duckweed over the period of a month.

In this graph the area, measured in square feet, starts out very small. It grows slowly until Day 22 or so. Then the surface starts increasing quickly. This type of growth is called exponential growth.

This graph shows the amount of remaining pie if half the remaining pie is eaten each day. We can see that there is one whole pie on Day 1. Then on Day 2, there is half of the pie left. Then on Day 3, half of a half, or one-fourth of the pie is remaining. Each day the amount of pie eaten gets smaller and smaller.

This type of graph is modeling exponential decay.