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  (d)  (-3, -7)

Step-by-step explanation:

Compare the given expression to vertex form ...

  (x -h)² +k

You see that h = -3 and k = -7.

The vertex is (h, k), so is (-3, -7).

x-intercept:

A line that crosses the graph at x-axis.

i.e substitute y = 0 and solve for x.

As per the statement:

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

Given the graph:

Substitute y = 0  we have;

⇒

⇒

⇒

⇒

⇒

By zero product property we have;

x-20 =0 and x+10 = 0

⇒x = 20 and x = -10

Therefore,  the x-intercept represents the water has no larvae at −10 degrees Celsius and 20 degrees Celsius.