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? The number of larvae is greatest at 450 degrees Celsius. The number of larvae is greatest at 5 degrees Celsius. The least number of larvae in the water is 450. The least number of larvae in the water is 5.

Answer 1

Answer:

The number of larvae is greatest at 5 degrees Celsius.

Answer 2

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

Given the equation $y= -2x^2 + 20x +400$

x is the temperature of water in degrees Celsius, and y is the number of insect larvae in the water

Peak of the graph is the vertex

Now we find out the vertex from the given equation

To find x coordinate of vertex we use formula x= $\frac{-b}{2a}$

a= -2, b= 20

So x= $\frac{-20}{2(-2)}$

x = $\frac{-20}{-4}$

x = 5

Now we find out y

Plug in 5 in the place of x

$y= -2(5)^2 + 20(5) +400$

y= 450

Vertex is (5,450)

It means the number of larvae reaches the maximum of 450 at 5 degree Celsius

Hence , the number of larvae is greatest at 5 degrees Celsius.