Answer: not sure how helpful this is, but the second one is correct (if it's the one that's corresponding to the blue line). The pink line, however, is incorrect if it is corresponding to the first equation. The first equation must have a y-intercept of 1.

Step-by-step explanation:

4 0

3 years ago

A new hospital tracked the number of births during its first 6 months of operation, as shown in the table. Find a quadratic func

UNO [17]

Let x refers to the Month numbers
And y refers to Number of births

There is 5 steps to find the quadratic function that models the data.

First step ⇒ Plot the data pairs (x, y) in a coordinate plane.
 which are the blue circles in the attached figure

Second step ⇒ Draw the parabola you think best fits the data.
 Which is the red function in the attached figure.

Third step ⇒ Estimate the coordinates of three points on the
 parabola, which are (2, 108), (4, 68), and (6, 75).
 which are the black squares in the attached figure

Fourth step ⇒ Substitute the coordinates of the points into the model 
 y = ax2 + bx + c
 to obtain a system of three linear equations.

 4a + 2 b + c = 108 ---------(1)
 16a + 4 b + c = 68 ---------(2)
36a + 6 b + c = 75 ---------(3)

Fifth step ⇒ Solve the linear system.
 By using the calculator
 a = 5.875 , b = -55.25 , c = 195

So, the quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
To predict the number of births for month 8
substitute with x = 8 ⇒ y = 5.875 * 8²- 55.25 * 8 + 195 = 129