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Lesson 9.5

Lesson 9.5. Objective: To solve quadratic equations using the quadratic formula. What formula can be used to solve any quadratic equation?. Quadratic formula: When. Then the value of x is…. Use the quadratic equation to solve for x. Example:. a = 1 b = 9 c = 14. Solve for x. Example:.

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Lesson 9.5

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  1. Lesson 9.5 Objective: To solve quadratic equations using the quadratic formula. What formula can be used to solve any quadratic equation? Quadratic formula: When Then the value of x is…

  2. Use the quadratic equation to solve for x. Example: a = 1 b = 9 c = 14

  3. Solve for x Example: a = 1 b = 5 c = -6

  4. Example: Solve for x a = -2 b = 6 c = 9 Simplify Simplified

  5. Vertical Motion Model A ball is thrown upwards with an initial velocity of 90 feet per second from a height of 6 feet. Use the vertical motion model to determine the time it will take the ball to hit the ground. h = height of ground t = time v = initial velocity s = starting height a = -16 b = 90 c = 6

  6. Applications of the Discriminant The discriminant is the expression inside the radical in the quadratic formula, b2 – 4ac. • If b2 – 4ac is positive, then the equation has two solutions. • If b2 – 4ac is zero, then the equation has one solution. • Ifb2 – 4acis negative, then the equation has no real solution.

  7. The discriminant also tells the number of times the parabola crosses the x-axis Positive discriminant: The parabola crosses x-axis twice. Zero discriminant: The parabola crosses x-axis once. Negative discriminant: The parabola never crosses x-axis. Positive Two solutions Negative No solutions Zero One solution

  8. Examples: Find the discriminant and determine the number of solutions a =1 b =-3 c =-4 1. 9 - -16 25 Two solutions a =1 b =2 c =5 2. 4 – 20 –16 No solutions 3. 16 – 16 0 One solution

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