Quadratic Function A function written in the form

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

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

PARABOLA Graph of a Quadratic Function Parabola Vertex 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. -9 minimum value Axis of symmetry x=7 A vertical line that divides a parabola into two parts that are mirror images. Equation: (7, -9) x value of the vertex

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

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. a. Find a quadratic model for the data. b. Use the model to estimate the height of the ball at 2. 5 seconds. c. After how many seconds will the ball be at 20 ft? Height of the Ball Time Height 0 s 1 s 2 s 3 s 46 ft 63 ft 48 ft 1 ft a. y = -16 x 2 + 33 x + 46 , where x is the number of seconds after release and y is height in feet. b. The ball will be 28. 5 ft after 2. 5 seconds. c. Approximately 2. 7 seconds.