PPT-5.9.1 – The Quadratic Formula and Discriminant

Recall we have used the quadratic formula previously Gives the location of the roots xintercepts of the graph of a parabola Function must be in standard form fx ax 2 bx c Example Find the roots for the function fx 2x. Given . a quadratic equation use the . discriminant. to determine the nature . of the roots.. What is the discriminant?. The discriminant is the expression b. 2. – 4ac.. The value of the discriminant can be used. Why do we use the discriminant?. The discriminant tells us one of two things:. How many roots/x-intercepts/zeros does a quadratic function have?. How many solutions does a quadratic equation have?. Example. This PowerPoint . was adapted from . http://. www.purplemath.com/modules/quadform2.htm. and . http://. teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/6-4/2006_6_4.ppt. Looking Back…. In our previous lesson, we solved quadratic function by . Get out a clean sheet of paper. Write your name at the top. . This will be turned in. .. Solve each equation by completing the square.. . .  . 4.6 Quadratic Formula. What THREE methods have we used so far to solve quadratics?. Page 3. General equation of a quadratic:. Quadratic Formula:. Notice where the letters come from for the formula. We use the quadratic formula when something can not be factored. However, it also works for factorable quadratic equations as well.. Section 3.4 beginning on page 122. The Big Ideas. The . quadratic formula . allows us to . solve any quadratic equation . once it is written in standard form. The . discriminant. . is a part of the quadratic formula that tells us . KFUPM - Prep Year Math Program (c) 20013 All Right Reserved. . Quadratic Equations . . Solving . Quadratic Equation. . . The . Discriminant. . Equations . that Quadratic in Form . Solve:. LINEAR . QUADRATIC . QUADRATIC . Quadratic Equations. Solve:. a) b) . . Learning Log Summary . LT. . 1. . – I can . solve. quadratic equations using factoring or the square root method.. Vocabulary. Discriminant - tells you how many solutions and what type you will have.. If the . discriminant is. . positive . – 2 real solutions. . negative . – 2 imaginary solutions. . zero . – 1 real solution. . for the given values:.  . 3. Sketch . the graph for each quadratic. No solutions One solution Two solutions. Using the Discriminant. I can . use the discriminant to determine how many solutions a quadratic equation will have.. There are many uses of parabolas in real-world applications.. Graphs of Quadratic Functions. Plotting quadratic curves. If you remember a relation is a correspondence between two sets of numbers called the . General Equation. Y = ax². What if A was positive?. Test in your calculator. What if A Was negative?. Test in your calculator.. Y = ax². What if A was greater than 1?. Test in your calculator. What if A Was less than 1?. #9. Topics:. Solving Quadratics by . Factoring . Square Root. Completing the Square. Quadratic Formula. Solving quadratics having complex solutions. Ways . to Solve a Quadratic Equation. The Quadratic Formula. Steven J Miller, Williams College (sjm1@Williams.edu). 1. https://web.williams.edu/Mathematics/sjmiller/public_html/math/talks/talks.html. Goals. Learn how to solve polynomial equations and see applications of polynomials and ways to find their roots..