A group of people in an art class and a crafts class were surveyed whether they exercise more than 5 hours a week or less than 5
hours a week. In the art class, 5 people exercise more than 5 hours a week and 8 people exercise less than 5 hours a week. In the crafts class, 10 people exercise more than 5 hours a week and 4 people exercise less than 5 hours a week.
What is the relative frequency of people who exercise more than 5 hours a week in the art class to the total number of people surveyed?
Round the answer to the nearest hundredth.
What is the relative frequency of people who exercise more than 5 hours a week in the art class to the total number of people surveyed?
Round the answer to the nearest hundredth.
1 answer:
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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.