1 / 6

Understanding Quadratic Functions: Classification and Applications

Learn to classify functions as linear or quadratic, identify terms, and model real-world scenarios with quadratic equations. Understand parabolas, vertices, and axis of symmetry. Apply quadratic models to solve problems.

paulmcdonald
Download Presentation

Understanding Quadratic Functions: Classification and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quadratic Functions

  2. Quadratic Function A function written in the form f(x) = ax2 + bx + c, where a 0. quadratic term linear term constant term

  3. Classifying Functions Determine whether each function is linear or quadratic. Identify the quadratic, linear and constant term. 1. f(x) = (x – 5)(3x – 1) 2. f(x) = (x2 + 5x) – x2 3. f(x) = x(x + 3) quadratic; 3x2, -16x, 5 Linear; none, 5x, none quadratic; x2, 3x, none

  4. PARABOLAGraph of a Quadratic Function Parabola Vertex Axis of symmetry A vertical line that divides a parabola into two parts that are mirror images. x = 7 The point at which the parabola intersects the axis of symmetry. The y value of the vertex represents the maximum or the minimum value of the function. Equation: (7, -9) -9 minimum value x value of the vertex

  5. Finding a Quadratic Model Find a quadratic model for each set of values. • (1, -2), (2, -2), (3, -4) • (1, -2), (2, -4), (3, -4) 3. (-1, 6), (1, 4), (2, 9) f(x) = -x2 + 3x – 4 f(x) = x2 – 5x + 2 f(x) = 2x2 – x + 3

  6. Real – World Connection A man throws a ball off the top of a building. That table shows the height of the ball at different times. • Find a quadratic model for the data. • Use the model to estimate the height of the ball at 2.5 seconds. • After how many seconds will the ball be at 20 ft? Height of the Ball • y = -16x2 + 33x + 46 , where x is the number of seconds after release and y is height in feet. • The ball will be 28.5 ft after 2.5 seconds. • Approximately 2.7 seconds.

More Related