QUADRATIC FUNCTIONS

Transform quadratic functions.

Describe the effects of changes in the coefficients of y = a(x – h)² + k.

Objectives

quadratic functionparabolavertex of a parabolavertex 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.

x f(x)= x2 – 4x + 3 (x, f(x))

0 f(0)= (0)2 – 4(0) + 3 (0, 3)

1 f(1)= (1)2 – 4(1) + 3 (1, 0)

2 f(2)= (2)2 – 4(2) + 3 (2,–1)

3 f(3)= (3)2 – 4(3) + 3 (3, 0)

4 f(4)= (4)2 – 4(4) + 3 (4, 3)

GRAPH BY USING A TABLE. Make a table. Make sure you plot enough ordered pairs to see both sides of the curve.

USE THE GRAPH OF (QUADRATIC PARENT FUNCTION) AS A GUIDE, DESCRIBE THE TRANSFORMATION AND THEN GRAPH EACH FUNCTION.

𝒈 (𝒙 )=(𝒙−𝟐 )𝟐+𝟒

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

𝒈 (𝒙 )=(𝒙+𝟐 )𝟐−𝟑

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

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.

The parent function is a vertically stretched by a factor of and then translated 2 units left and 5 units down to create g(x).

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 dm(t)= 0.8t². What kind of transformation describes this change from d(t)= 4.9t², and what does the transformation mean?