PPT-How do you find the maximum value of a quadratic function?

For example y3x 2 18x25 In this lesson you will learn to rewrite a quadratic function to reveal the maximum value by completing the square Suppose we have y3x 2 18x25 is negative. 2.3 Linear Functions. 2.4 Quadratic Functions. 3.1 Polynomial and Rational Functions. 2.3 Slopes of Lines. A function that can be written in the form f(x) = mx + b is called a . linear function . because its graph is a straight line. . 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. Recall, we have used the quadratic formula previously. Gives the location of the roots (x-intercepts) of the graph of a parabola. Function must be in standard form; f(x) = ax. 2. + . bx. + c. Example. Find the roots for the function f(x) = 2x. 1) 2a – b. 2. c. 2) . b. 2. – 4ac. 2a. Graph each function.. 3) y = x. 2. Factor each expression.. 4) 4x. 2. 4x 1. 5) m. 2. – 7m – 18. Chapter 9: . Quadratic Functions and Equations. Quadratic Equations and their Applications. Standard 14: Graph and analyze quadratic functions.. Domain and Range. X and Y intercepts. Maximum or Minimum Values. Intervals of increasing and decreasing. Warm Up. Find the . x. -intercept of each function.. 1.. . f(x. ) = –3. x. 9. 2.. . f. (. x. ) = 6. x . 4. Factor each expression.. 3.. 3. x. 2. – 12. x. 4.. . x. 2. – 9. x. 18. 5.. Section 2.2 beginning on page 56. By the End of This Section …. You will be able to identify key aspects of the graph of a function based on its equation in vertex form, intercept form, and standard form. . 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?. Quadratic Function. A . quadratic function . is defined by a quadratic or second-degree polynomial.. Standard Form. , . where . a. . ≠ 0. .. Vertex Form. , where a. . ≠ 0..  . Vertex and Axis of Symmetry. 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. 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 :. ACT. Objectives . F-IF.4: For . a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. .