PPT-3.2-1 Vertex Form of Quadratics

Recall A quadratic equation is an equationfunction of the form fx ax 2 bx c Vertex Form To facilitate an easier way to graph we can look at the vertex form of a quadratic Vertex. 1. Find the solution(s): 2. Solve and graph the inequalities: 3. What model best fits the data: . f. (x) = x. 2. + 2x + 1 3 < x + 1 < 15. g. (x) = . Solve each equation.. 1.. 27 = . x. 2. + 11 . 2.. . x. 2. = 48 . 3.. 84 = 120 – . x. 2. Ellipses - Warm Up. 1.. 27 = . x. 2. + 11. 16 = . x. 2. . x. = . ± 16 = ±4. Definition or Depiction. Linear Function: . f(x) = . mx+b. Makes a line. Constant change in y for each change in x . Quadratic Function: . Standard Form: f(x) = x. 2. +bx+c or . Vertex Form: f(x) = a(x-h). Factor: 3x. 2. + 10x + 8. Factor and Solve: 2x. 2. - 7x + 3 = 0. Math I. UNIT QUESTION: What is a quadratic function?. Standard: . MM2A3, MM2A4. Today’s Question:. How do you graph quadratic functions in vertex form?. Writing equations in vertex form. Because the vertex is translated . h. horizontal units and . k. . vertical from the origin, the vertex of the parabola is at (. h. , . k. ).. Hint: Vertical stretch makes the parabola skinnier.. Section 3.3 Beginning on page 112. The Big Idea. Completing the square . is a technique we can use to write a quadratic in vertex form.. Completing the square is creating a . Perfect Square Trinomial. 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. Richardson 423. Math 2. Quadratics: What’s the big deal?. In this chapter of Math 2 we will be covering Quadratics. In the previous lesson we learned to quantify groups of terms, exponents, and multiple variable problems.. Unit 5 . Conics... The parabola is the locus of all points in a plane that are . the same distance from a line in the plane, the . directrix. , . as from a fixed point in the plane, the . focus. .. Point Focus = Point Directrix. Expanding. Brackets. Factorising. Expanding . Double . Brackets. Solving . Linear . Equations. Plotting graphs by. substitution into . equations. Solving . Quadratic. Equations. Solving . Quadratics. 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?. complete the square. If you have an equation in the form h = -2.25x. 2. 4.5x 6.75, where ‘h’ is height, how do you find the maximum height?. 1. st. , factor out -2.25:. Take out: . HW. Packet. Quiz from . fri. . SWBAT: Solving quadratics by completing the square . -8. -8. 2(x-2). 2. = -12. 2. 2. (x-2). 2. = -6.  . x-2 = ±. i.  . +2. +2. x = 2 ± . i.  . SWBAT: Solving quadratics by completing the square . 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.