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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 do the x-intercepts of the graph represent?

There were 20 larvae in the water at 0 degrees Celsius.
There were 10 larvae in the water at 0 degrees Celsius.
The water had no larvae at −10 degrees Celsius and 20 degrees Celsius.
The water had maximum larvae at −10 degrees Celsius and 20 degrees Celsius.

Respuesta :

The x-intercepts of the graph represents the water had no larvae at −10 degrees Celsius and 20 degrees Celsius. The correct option is C.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the function y=-2x²+20x+400, where x represents the temperature of water and y represents the number of insect larvae.

Now, to find the y-intercept of the function substitute the function against 0.

y = 0

-2x² + 20x + 400 = 0

-2x² + 40x - 20x + 400 = 0

-2x(x - 20) - 20(x - 20) = 0

(-2x - 20)(x - 20) = 0

-1(2x + 20)(x-20) = 0

x = -20/2 = -10

x = 20

Thus, the x-intercepts of the graph represents the water had no larvae at −10 degrees Celsius and 20 degrees Celsius. This is because at x-intercept the value of y or the population of the insect larvae will become zero, while the temperature still exist.

Hence, the x-intercepts of the graph represents the water had no larvae at −10 degrees Celsius and 20 degrees Celsius.

Learn more about Function here:

https://brainly.com/question/5245372

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Answer: The water had no larvae at −10 degrees Celsius and 20 degrees Celsius.

Step-by-step explanation:

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