Question

DQuestion 19 28 pts Problem 2. Quadratic Equations A quadratic equation has the form: a bc0 The two solutions are given by the formula: 2a Write a program with a loop that a) solves quadratic equations with coefficients read from the terminal, b) visualizes the corresponding quadratic function az2 brc0using the matplotlib module. Instructions Write all code for this problem in a file p2.py 1. The program consists of a main whtle loop (an infinite loop) in which the user is prompted to enter values for coefficients a, b, and c. Assume the user types valid float numbers from the terminal. The program converts the input to float type and then uses formula (1) above to compute solutions x and x2, as follows: a. if D-24ac0 then the solutions are complex numbers (i.e. not real) and the program displays the string "no real solutions b. if D-0 then xi-r2 and the program displays: "one solution: “ followed by the value x. c.ifD> 0 then the solutions are distinct and the program displays "two solutions:"followed by the values of x1 and x2 To stop the loop and to end the program, the user enters a-0. 2. Within the main loop, after displaying the values of the real solutions (if any) the program must display the graphic of the quadratic function on the [-5, 5] domain. For that, use the matplotlib Python module. Within a nested whtle loop populate a list of floats in variable xs with 100 float numbers between -5 and +5 as shown in the lecture and append to a list ys the matching function values Then, use the matplotlib.pyplotplorO function to generate the plot and the showO function to display the graphic figure. Make sure the function line is displayed with a blue line and dots. 3. Take a screenshot of the PC desktop showing the Spyder Python shell and the matplotlib figure window and save the screenshot image file The screenshot may look similar to this one

Answer 1

# TEXT CODE

# import matplot module
import matplotlib
# import math library
import math

# initialize variable c = 1 to keep track the number of plots plotted
c = 0
# start main while loop
while True:

# get value of coefficient a
a = float(input("Enter value of coefficient 'a' ( Enter 0 to quit ) : "))

# if a is 0 break
if a == 0: break

# get value of coefficient b
b = float(input("Enter value of coefficient 'b': "))

# get value of coefficient c
c = float(input("Enter value of coefficient 'c': "))

# calculate D (using formula D = b^2 - 4ac)
D = b*b - 4*a*c

if D < 0:
print("\nNo real solutions")
# continue main while loop
continue
  
if D == 0:
# calculate root x1
x1 = (-b)/(2*a)
print("\none solution: ", x1)

if D > 0:
# calculate root x1
x1 = (-b + math.sqrt(D))/(2*a)
# calculate root x2
x2 = (-b - math.sqrt(D))/(2*a)
print("\ntwo solutions:", x1, " ", x2)

# initialize xs to empty list
xs = []

# initialize ys to empty list
ys = []

# initialize i to -0.5(this is be used in below nested while loop )
i = -5.0
# nested while loop to generate 100 flaoting points number
while i < 5.0:
# store i into x
x = i
  
# append x to xs
xs.append(x)

# append value of (ax^2 + bx + c) int ys
ys.append(a*(x**2) + b*x + c)

# get next floating point number (trucate to one decimal point)
i = float('%.1f'%(i + 0.1))
  
# plot the function line in "blue" line and "dots" passing third argument "b." in function plot()
matplotlib.pyplot.plot(xs, ys, "b.")
matplotlib.pyplot.xlabel("x")
matplotlib.pyplot.ylabel("y")
  
# get the title as figure number( str(c) has been used to convert int c to string )
title = "figure" + str(c)
  
# assign the title to plot
matplotlib.pyplot.title( title )
  
# show the plot
matplotlib.pyplot.show()
  
# increase value of variable c by 1 (remember c keeps track of plot number )
c = c + 1

SCREENSHOTS:

code:

# inport matplot module import matplotlib # inport math library import math # initialize variable c 1 to keep track the number of plots plotted # start nain while loop while True: 16 # get value of coefficient a float(input("Enter value of coefficient 'a' ( Enter θ to quit ) : ")) 12 a 13 # if a is θ break if a break 15 16 # get value of coefficient b 18 bfloat(input("Enter value of coefficient 'b: ")) # get value of coefficient c 21 cfloat(input("Enter value of coefficient 'c:")) 23 24 # calculate D (using formula D-b^2-4ac) 25 27 print("nNo real solutions") # continue main while loop continue 28 29 # calculate root x1 print("\none solution

37 if DO 38 # calculate root x1 x1 - (-b nath.sqrt(D)/(2 a) # calculate root x2 x2 - (b- math.sqrt(D))/(2*a) print("ntwo solutions:", xi, "", x2) 41 42 44 45 # initialize xs to empty list xs # initialize ys to empty list 48 ys [ 49 se # initialize i to -9.5(this is be used in below nested while loop ) 52 # nested while loop to generate 188 flaoting points number while i < 5.0: # store i into x 56 57 58 # append x to xs xs.append(x) # append value of (ax^2 + bx + c) ys . append(a*(x**2) + b*x + c) int ys 61 62 # get next floating point number (trucate to one decimal point) 63 66 # plot the function line in "blue" line and "dots', passing third argument "b matplotlib.pyplot.plot(xs, ys, "b.") in function plot() 67 68 matplotlib.pyplot.xlabel("x") 69 matplotlib.pyplot.ylabel( "y") 76 71 # get the title as figure number( str(c) has been used to convert int c to string ) title"figure" str(c) 72

73 74 # assign the title to plot 75 matplotlib.pyplot.title title ) 76 77 # show the plot 78 matplotlib.pyplot.show() 79 # increase value of variable c by 1 (renenber c keeps track of plot number 86 81

output:

f coeffictent 'aEnter e to qutt:1 Enter value of coefficient 'a' ( Enter e to quit ) : 1 Enter value of coefficient 'b' 4 Enter value of coefficient 'c': two solutions :6.0-4.9 figure0.0 40 30 20 10 -2 Enter value of coefficient 'a' ( Enter θ to quit ) : 2 Enter value of coefficient 'b':4 Enter value of coefficient 'c 2 one solution: -1.8

igure2.0 70 60 50 40 30 20 10 Enter value of coefficient 'a' ( Enter to quit ) : e