Question

A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water: graph of y equals minus 2 times the square of x plus 20 times x plus 400 What does the peak of the graph represent?

Answer 1

Answer: The number of larvae in the water is greatest at 5 degrees Celsius.

Explanation:

Answer 2

The maximum number of larvae occurs when the temperature is 5°C.

Explanation:

We are given the function
`y=-2x^2+20x+400`,

where x= temperature of water (in degrees) and y= number of insect larvae in water.

From the graph of the function below, we see that,

The peak or the highest point of the parabola is (5,450).

That is, when x= 5, then the value of y= 450

That is, when the temperature of the water is 5°, then the number of larvae in water is 450.

Hence, the peak of the graph means that,

The maximum number of larvae occurs when the temperature is 5°C.