PPT-Quadratic models Warm Up

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. 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.. Mary has (4x +10) dollars and Ron has (-5x + 20) dollars. How much more money does Mary have than Ron?. The measure of the perimeter of a triangle is (37m+42). It is known that two of the sides of the triangle have measures of (14m +16) and (10m +20). Find the length of the third side. . Hubarth. Algebra. Standard Form of a Quadratic Function. A quadratic function is a function that can be written in the form . , . where a, b, and c are real numbers and a. 0. This form is called standard form of a. Essential Questions . and Quadratics review. Function, relation, domain, range, perfect square trinomial, difference of perfect squares, roots/zeroes, real and complex roots, extrema, minimum, maximum, y-intercept, line or Axis of symmetry, standard form, vertex form, intercept form, 1. 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). . 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?. 1.. 6 units down. 2.. 3 units right. (–2, –1). (1, 5). For each function, evaluate . f. (–2), . f. (0), and . f. (3).. 3.. . f. (. x. ) = . x. 2 . 2. x. 6. 4.. . f. (. x. ) = 2. x. 2 . December 5. , 2016. Quadratic functions are polynomial equations that have an __________ in the equation and ____________ is the highest exponent of x. . The standard form of a quadratic equation is :. 2x. 2. – 4x(3x – 5). 3x(x – 2). (x – 2)(x + 5). (-4x + 3)(2x – 7). 3x(2x – 7) + 6x(4x + 5). x(1 – x) – (1 – . 2x. 2. ). (5x + 3). . 2. -7x(. 5x. 2. . – . 4x). (. 4x. . – . 5) (-2x. 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..