On a piece of paper, complete #’s 1 − 4. Check your answers along the way.

• Graph the quadratic equation below on a piece of graph paper, or on your graphing calculator, and find its roots.
  
  y = x^2 + 2x − 8
  
  
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• Given the ordered pairs in the table below, find the roots of the quadratic function.
  
  
  
  
• Given the graph below, find the roots of the function.

The height of an object projected into the air is described by the quadratic function h(t) = -16t² + 32t, where h(t) is the height of the object in feet t seconds after it is projected.

When does the object reach the ground?

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It takes the object 2 seconds to reach the ground. You can either find this by graphing h(t) = -16t² + 32t or by factoring the equation.  You can see by graphing that the quadratic function will cross the x-axis at t = 0 and t = 2. Factoring will give you h(t) = -16t(t + 2).  In this case if t = 0 or t = 2, both would give you h(t) = 0. Therefore both are roots of this function.