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. Grades C to A*. Hyperlinks!. Expanding a single bracket. Solving quadratics by factorising. Factorising quadratic expressions. Factoring expressions. Multiplying out 2 brackets. Quadratic simultaneous equations. 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. 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 . Linear Discriminant Analysis. Objective. -Project a . feature space (a dataset n-dimensional samples) onto a smaller . -Maintain . the . class separation. Reason. -Reduce computational costs. -Minimize . 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. Standards 8-10. Graphs of Quadratic Functions . U- Shaped Graph . Vertical y=x. 2. or Horizontal x=y. 2. Positive Negative . Summary: The of a Quadratic Function is U shaped. . Positve. Find the roots:. 1) x. 2. – 64 = 0 . 2) 8x. 2. – 64x = 0. 3) x. 2. – 16x + 64 = 0. 1) Ensure the quadratic equation is set to zero.. 2) Factor the quadratic equation (GCF, perfect square binomial [DOTS], trinomial). . (. not. including the radical sign) in the quadratic formula is called the . . , . D. , of the corresponding quadratic equation, . ..  . The discriminant allows you to determine the nature of the roots of the equation because. Tammy Wallace. Varina High. What is a Quadratic Equation?. A . QUADRATIC EQUATION. is an equation in which the greatest power of any variable is 2. . The standard form of a quadratic equation is . 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?. Solve each system of equations.. a = . 0, . b. = –5. . 1. . 2. . 3. . 2. a. – 6. b. = 30. 3. a. . b. = –5. 2. a. – 5. b. = 16. 4. a. – 2. b. = 8. a. . b. = 6. 9a 3b = 24. #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..