QUADRATIC FUNCTIONS

Transform quadratic functions. Describe the effects of changes in the coefficients of y = a(x – h)² + k. Objectives quadratic function parabola vertex of a parabola vertex form Vocabulary

A quadratic function is a function that can be written in the form of f(x) = a (x – h)² + k (a ≠ 0). In a quadratic function, the variable is always squared. The graph of the parent function f(x) = x² is a U-shaped curve called a parabola. As with other functions, you can graph a quadratic function by plotting points with coordinates that make the equation true. This lowest or highest point is the vertex of the parabola. The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.

xf(x)= x 2 – 4x + 3(x, f(x)) 0f(0)= (0) 2 – 4(0) + 3(0, 3) 1f(1)= (1) 2 – 4(1) + 3(1, 0) 2f(2)= (2) 2 – 4(2) + 3(2,–1) 3f(3)= (3) 2 – 4(3) + 3(3, 0) 4f(4)= (4) 2 – 4(4) + 3(4, 3) Make a table. Make sure you plot enough ordered pairs to see both sides of the curve.

USE THE QUADRATIC PARENT FUNCTION AS A GUIDE TO DETERMINE THE TRANSFORMATION OF THE FUNCTION THEN GRAPH.

USE THE QUADRATIC PARENT FUNCTION AS A GUIDE TO DETERMINE THE TRANSFORMATION OF THE FUNCTION.

USE THE DESCRIPTION TO WRITE THE QUADRATIC FUNCTION IN VERTEX FORM.

APPLICATION PROBLEM On Earth, the distance d in meters that a dropped object falls in t seconds is approximated by d(t)= 4.9t². On the moon, the corresponding function is d m (t)= 0.8t². What kind of transformation describes this change from d(t)= 4.9t², and what does the transformation mean?