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1 answer:
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Answer: 0.796 meters
Step-by-step explanation:
Circumference of circle = , where r=radius
Here, Circumference of loop = 2.5 meters
i.e.
Diameter = 2r = 2(0.398) = 0.796 meters
Hence, The diameter of Taiga's exercise hoop = 0.796 meters
Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far: 
. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides. 
. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process. 
. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.