13 the box plot below summarizes the data for...
13 the box plot below summarizes the data for the amount of snowfall, in inches, during the winter of 2021 for 12 locations in western new york.\nwinter of 2021 snowfall (inches)\nwhat is the interquartile range?\n(1) 30\n(2) 50\n(3) 80\n(4) 110\n14 four quadratic functions are represented below.\na(x)=(x - 3)^2 - 7\nc(x)=x^2 + 6x + 3\nwhich function has the smallest minimum value?\n(1) i\n(2) ii\n(3) iii\n(4) iv
Answer
### Explanation:
#### Step1: Recall inter - quartile range formula
The inter - quartile range (IQR) is \(Q_3 - Q_1\). In a box - plot, the left - hand side of the box is \(Q_1\) and the right - hand side of the box is \(Q_3\). From the box - plot, \(Q_1 = 40\) and \(Q_3 = 90\).
#### Step2: Calculate the IQR
\(IQR=Q_3 - Q_1=90 - 40 = 50\)
#### Step3: Find minimum values of quadratic functions
- For \(a(x)=(x - 3)^2-7\), since \((x - 3)^2\geq0\), the minimum value occurs when \(x = 3\) and \(a(3)=-7\).
- For \(b(x)\) from the graph, the vertex is at \((0,-4)\), so the minimum value of \(b(x)\) is \(-4\).
- For \(c(x)=x^{2}+6x + 3\), we complete the square: \(c(x)=(x + 3)^{2}-9 + 3=(x + 3)^{2}-6\). The minimum value occurs when \(x=-3\) and \(c(-3)=-6\).
- For \(d(x)\) from the table, the minimum value is \(-5\).
### Answer:
13. (2) 50
14. (1) I