Investigation: When is a Quadratic Function Positive?

Glossary Checklist FAQ

When is a Quadratic Function Positive?

1. Consider the function \(f(x) = -x^2 + 2x + 5\).
   
   
1. Complete the table below.
   
   

   \(x\)	Is \(f(x)\) positive?
   \(-5\)	no
   \(-4\)
   \(-3\)
   \(-2\)
   \(-1\)
   \(0\)
   \(1\)
   \(2\)
   \(3\)
   \(4\)
   \(5\)

   
   
2. Describe a pattern in the table.
   
   
   
3. Graph the function. How is the graph related to the pattern in the table?
   
   
2. Consider the function \(f(x) = (x + 2)(x - 3)\).
   
   
1. What \(x\)-values make \(f(x)\) positive? Can this be answered without graphing or using a table of values?
   
   
   
2. Sketch a number line representing the \(x\)-values that make \(f(x)\) positive.
   
   
   
3. Sketch the graph of \(y = f(x)\). How is the information in the graph related to the information from parts a and b?