Presentation on theme: "Solving Quadratic Equations Using the Quadratic Formula"— Presentation transcript:
1 Solving Quadratic Equations Using the Quadratic Formula 11.2Solving Quadratic Equations Using the Quadratic Formula1. Solve quadratic equations using the quadratic formula.2. Use the discriminant to determine the number of real solutions that a quadratic equation has.3. Find the x- and y-intercepts of a quadratic function.4. Solve applications using the quadratic formula.
2 Coefficient of squared term is NOT 1. Solve:Coefficient of squared term is NOT 1.squaredQuadratic Formula
3 Quadratic FormulaTo solve ax2 + bx + c = 0, where a 0, use
4 2 real rational solutions Solve:a = 2, b = –7, c = 32 real rational solutions
5 2 real irrational solutions Solve:a = 1, b = –2, c = –11.21116 ∙32 real irrational solutions
6 2 non-real complex solutions Solve:a = 1, b = -4, c = 52112 non-real complex solutions
9 Methods for Solving Quadratic Equations When the Method is Beneficial1. FactoringUse when the quadratic equation can be easily factored.2. Square root principleUse when the quadratic equation can be easily written in the formNo middle term.3. Completing the squareRarely the best method, but important for other topics.4. Quadratic formulaUse when factoring is not easy, or possible.
10 What made the difference? The Discriminant 2 non-realcomplex solutions2 real rationalsolutions2 real irrationalsolutionsWhat made the difference?The Discriminant
11 Discriminant:The discriminant is the radicand, b2 – 4ac, in the quadratic formula.The discriminant is used to determine the number and type of solutions to a quadratic equation.
12 2 non-real complex solutions 2 real rational solutions 2 real irrationalsolutionsIf the discriminant is….there will be….positive and a perfect square2 real rational solutions. There will be no radicals left in the answer. The equation could have been factored.positive but not a perfect square2 real irrational solutions. There will be a radical in the answer.1 real rational solution.negative2 non-real complex solutions. The answer will contain an imaginary number.
13 Evaluate the discriminant: b2 – 4ac. Use the discriminant to determine the number and type of solutions.Evaluate the discriminant: b2 – 4ac.a = 2, b = 5, c = 1Discriminant:Positive but not a perfect square.Two real irrational solutions.