11.3: Quadratic Formula
This activity is intended to supplement Algebra I, Chapter 10, Lesson 5.
Problem 1
1. Identify the zeros of \begin{align*}y = x^2  4\end{align*}
2. You may already know the zero product property, and can demonstrate why the following are the solutions to the equation above:
\begin{align*}x + 2 = 0\end{align*}
3. A program, QUAD, is provided that has the Quadratic Formula defined. Use \begin{align*}A = 1, B = 0\end{align*}
Problem 2
4. Now, examine the graph of \begin{align*}y = x^2 + x  6\end{align*}
Use the QUAD program again. You only need to enter in the correct values for \begin{align*}a, b\end{align*}
5. What are the solutions to the equation \begin{align*}y = x^2 + x  6\end{align*}
Problem 3
6. Now, examine the graph of \begin{align*}y = x^2  4x + 4\end{align*}
7. Using the QUAD program, what are the solutions to the equation \begin{align*}y = x^2  4x + 4\end{align*}
Exercise 4
8. Explore \begin{align*}y = x^2  2x  7\end{align*}
 “Some quadratic equations are not factorable with integers because…”
or
 “Quadratic equations are only factorable with integers when…”
9. Solve the following equations using the QUAD program.

\begin{align*}y = x^2  2x  7\end{align*}
y=x2−2x−7 
\begin{align*}y = 3x + x +3\end{align*}
y=−3x+x+3
10. Finally, use Lists to calculate the value of the discriminant for the previous two problems, whose solutions were irrational. Enter the \begin{align*}A\end{align*}

\begin{align*}y = x^2  2x  7\end{align*}
y=x2−2x−7 Solution: __________________ 
\begin{align*}y = 3x + x +3\end{align*}
y=−3x+x+3 Solution: __________________
Extensions/Homework
Use the formula in \begin{align*}L_4\end{align*}

\begin{align*}y = x^2  6x + 9\end{align*}
y=x2−6x+9 
\begin{align*}y = 3x^2 + 4x + 5\end{align*}
y=3x2+4x+5 
\begin{align*}y = 4x^2 + 2x + 2\end{align*}
y=−4x2+2x+2 
\begin{align*}y = 7x^2 + x  8\end{align*}
y=7x2+x−8 
\begin{align*}y = 2x^2  5\end{align*}
y=2x2−5
Look at the flow chart below and discuss with another student how to use it to answer these homework problems.