1. Use the discriminant to find the number of solutions
Solving Quadratic Equations using the QUADRATIC FORMULA
X =
If using algebra and square roots, or factoring and ZPP don’t work, you can ALWAYS find solutions to a quadratic equation in standard form ax2 + bx + c = 0 using the Quadratic Formula. It is a method that will ALWAYS work!
Remember: Solutions are where the graph crosses the x-axis.
There may be: one solution two solutions no solutions
Steps:
1) Example #1 2) 3)
Make sure the quadratic is in standard form first, then identify a, b and c
Use the discriminant to find
the number of solutions
Use the quadratic formula to
find the solutions.
Use a calculator to round to the
nearest hundredth if necessary.

2. 2. 4. Suppose a football player kicks a ball and gives it an
initial upward velocity of 47 ft/s. The starting height of the
football is 3 ft. If no one catches the football, how long
will it be in the air?
Use the vertical motion formula:
(The initial upward velocity is v, and the starting height is c.) 3.