The graph shown depicts the amount of snow accumulation from midnight to 5:00 am. The x-axis represents time (hours after midnig
ht), and the y-axis represents the number of inches of snow on the ground. How many inches of snow accumulated between 2:00 am and 5:00 am? A. 2.5 B. 0.75 C. 1.5 D. 1.25
1 answer:
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Recall that the vertex form of a quadratic function (or parabolic function) is equal to
Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.
One concept that we must remember when completing the square is that
(a + b)² = a² + 2ab + b²
So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.
So, going back to the function, we have
Thus, we have derived the vertex form of the function.
Answer: f(x) = (x + 7)² - 9
Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.
One concept that we must remember when completing the square is that
(a + b)² = a² + 2ab + b²
So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.
So, going back to the function, we have
Thus, we have derived the vertex form of the function.
Answer: f(x) = (x + 7)² - 9