Manny observed a Northern Gannet, a deep diving seabird, hovering at a height of 10 meters above the ocean surface. The bird then dove into the water, diving to a depth of 16 meters before coming to the surface. The dive can be modeled by a quadratic function, y = x2 – 10.3x + 10, where x represents the time the dive lasted in seconds and y represents the height of the bird in meters. Use the graphing calculator to graph the equation. After how many seconds did the bird surface? Round your answer to the nearest tenth.

We have been given an equation that represents dive of a bird as [tex]y=x^2-10.3x+10[/tex], where x represents the time the dive lasted in seconds and y represents the height of the bird in meters.

We can see that our given equation is a parabola. The leading coefficient is positive, so our parabola will be an upward opening parabola.

Upon graphing our given equation, we will get our required graph as shown in the attachment.

As x represents the time the dive lasted in seconds and y represents the height of the bird in meters, so the bird will be at the surface when the graph will cross x-axis.

We can see that graph crosses x-axis at [tex]x=1.085\text{ and }x=9.215[/tex].

Upon rounding to nearest tenth, we will get:

[tex]x\approx 1.1\text{ and }x=9.2[/tex].

At [tex]x\approx 1.1[/tex] the bird dives in water and goes down the water surface and at [tex]x=9.2[/tex] the bird comes to the surface, therefore, the bird will be at surface after 9.2 seconds.

adefioyelaoye adefioyelaoye · Answer 2 · 2022-04-25T17:58:41+02:00

The bird reached the surface of the water after 9.2 seconds.

What is a Parabola?

This is defined as a plane curve which is mirror-symmetrical and is approximately U-shaped.

From the graph, the given equation is = x² – 10.3x + 10

X represents the time the dive lasted in seconds and y represents the height of the bird in meters.

This means that the bird will be at the surface when the graph will cross x-axx-axis which is at x= 1.085 and x=9.215.

This means that the time taken for the bird to dive in is 1.1s while the time taken to reach the surface is 9.2s.

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