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5.5 The Quadratic Formula Algebra 2 27 5.5 THE QUADRATIC FORMULA Learning Targets: 1. Use the quadratic formula to solve 2 0 ax bx c . 2. Use projectile motion equation 2 0 0 16 h t v t h   to find when a projectile hits the ground. 3. Understand the relationship between the solutions to a quadratic equation and the x -intercepts of the parabola. 4. Use the discriminant to determine the number of solutions to an equation. Example 1 : Use completing the square to solve the equation 2 0 ax bx c . The solution to example 1 is known as the quadratic formula. ___________________________________ Example 2 : Use the quadratic formula to solve the following equations: a) 2 5 14 0 x x b) 2 14 10 x x c) 2 3 6 7 5 x x The height of a projectile can be modeled by the equation 2 0 0 16 h t v t h   , where 0 v = initial velocity and 0 h = initial height. If an object is dropped then 0 v = 0. If an object is launched from the ground, 0 h = 0.

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