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Hi there!
We can find the range using completing the square:
y = -x² - 2x + 8
Factor out a -1:
y = -(x² + 2x) + 8
Use the first two terms. Take the second term's coefficient, divide by 2, and square:
y = -(x² + 2x + 1) + 8
Remember to add by 1 because we cannot randomly add an additional number into the equation:
y = -(x² + 2x + 1) + 8 + 1
Simplify:
y = -(x + 1)² + 9
Since the graph opens downward (negative coefficient), the range is (-∞, 9)
Answer:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
Step-by-step explanation:
For this case we have the following data given:
Demand (x): 10,20,30,40,50,60,70,80,90,100
Price (y): 141 , 133,126, 128,113,97, 90, 82,79,53
We want to construct a linear model like this:
For this case we need to calculate the slope with the following formula:
Where:
So we can find the sums like this:
With these we can find the sums:
And the slope would be:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by: