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*} Solution: __________________
 \begin{align*}y = 3x + x +3\end{align*} Solution: __________________
Extensions/Homework
Use the formula in \begin{align*}L_4\end{align*} (above) to calculate the Discriminant for several other quadratics. Decide if the equation is factorable using integers, then solve it. Factor the quadratic if possible, if not, solve by the quadratic formula.
 \begin{align*}y = x^2  6x + 9\end{align*}
 \begin{align*}y = 3x^2 + 4x + 5\end{align*}
 \begin{align*}y = 4x^2 + 2x + 2\end{align*}
 \begin{align*}y = 7x^2 + x  8\end{align*}
 \begin{align*}y = 2x^2  5\end{align*}
Look at the flow chart below and discuss with another student how to use it to answer these homework problems.
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