Project 1 input/output commands

1. Problem Statement:
The goal of this programming assignment is to give students experience with
input/output commands and basic numerical calculations in C++. Specifically, your
program should do the following:
• Print a message asking the user to enter the A,B,C coefficients of a quadratic
equation: y(x) = A*x^2 + B*x + C. Save these values in three variables.
• Calculate and print the two roots of the quadratic equation using the classic
quadratic formula (see https://en.wikipedia.org/wiki/Quadratic_formula). For
this program, you can assume the user will always enter A,B,C values that result
in a positive discriminant value, so no error checking is needed.
• Calculate and print the X value that is halfway between the two roots of the
quadratic equation. If we are lucky, this should be the X location where the
quadratic curve has a local maximum or local minimum.
• Prompt the user to enter an X value. Read this value and calculate and print the
corresponding value of y(x) using the quadratic formula above.
• Prompt the user to enter a second X value. Read this value and calculate and
print y’(x) using the first derivative of quadratic formula: y’(x) = 2*A*x + B.
2. Design:
Your first design task is to decide how to calculate the two roots of the quadratic
equation. For this, you will need to look up the classic quadratic formula and think
about the sequence of operations you need to perform to calculate these values. To
implement the square root operation, you will need to call the sqrt() function that is
part of the <cmath library.
Your next task is to decide what sequence of operations are needed to evaluate the
quadratic equation at a given X value. Your final design task is to decide what
sequence of operations are needed to evaluate the derivative of the quadratic
equation at a given X value. Make sure you explain your design decisions in your
code using comments and again later in your project report.
3. Implementation:
Since you are starting with a "blank piece of paper" to implement this project, it is
very important to develop your code incrementally writing comments, adding code,
compiling, debugging, a little bit at a time. This way, you always have a program that
"does something" even if it is not complete.As a first step, it is always a good idea to start with an empty main function, and add
the code to read input data from the user, and then simply print these values back
out again. Once this part is working, you can start performing calculations with the
input data.
4. Testing:
Test your program to check that it operates correctly for all of the requirements
listed above. To verify that you are calculating roots properly, you may want to use
A,B,C values where you know the location of the roots in advance. For example,
quadratic equations of the form: y(x) = (x-a) * (x-b) = x^2 - (a+b)*x + a*b will have
two roots at x=a and x=b.
You are NOT required to add error checking in this program, but it is always good to
test a program to see what happens if the user inputs unexpected data (like “hello
mom”) or if the user enters A,B,C values that result in a negative discriminant. You
should cut/paste these results into your project report to document what your
program does in these cases.
5. Documentation:
When you have completed your C++ program, write a short report using the
“Programming Project Report Template” describing what the objectives were, what
you did, and the status of the program. Does it work properly for all test cases? Are
there any known problems? Save this project report in a separate document to be
submitted electronically.