04-1a+-+Using+Transformations+to+Graph+Quadratic+Functions

//Using Transformations to Graph Quadratic Functions//
Objective: We will be able to transform quadratic functions from the parent function, and describe the effects of changes in the coefficients of f(x) = a(x-h)2 + k

The parent quadratic function is f(x) = x2. Quadratic functions are written in the form f(x) = a(x - h)2 + k where a ≠ 0. In a quadratic equation, there is always a squared term. The table below shows a comparison between linear and quadratic parent functions.



The graph of a quadratic function is a U-shaped curve called a //**parabola.**//

Although we only need two points to draw the graph of a linear function, we need a greater number of points to correctly draw a graph of a quadratic function.

The graph is symmetrical about a line; the parent function is symmetrical about the y-axis, but once a transformation takes place, the line of symmetry may change.

To graph a quadratic function, we generate a table of values and plot the points. Then, we connect the points with a smooth curve.

 Let's look at an example:

If we are asked to graph the function f(x) = x2 - 4x + 3, we make a table, select values for x, and calculate the value of the function at that point.



<span style="display: block; font-family: Verdana,Geneva,sans-serif; font-size: 120%;">Be sure to choose points that reflect the symmetry of the graph. In this case, the parabola is translated three units to the right, so we choose points on both sides of 3 so we can see the symmetry. Look at the y coordinates to see the pattern. The graph will look like this: <span style="display: block; font-family: Verdana,Geneva,sans-serif; font-size: 120%;"> <span style="display: block; font-family: Verdana,Geneva,sans-serif; font-size: 120%;"> <span style="display: block; font-family: Verdana,Geneva,sans-serif; font-size: 120%;"> <span style="font-family: Verdana,Geneva,sans-serif;">﻿Proceed to Transforming Parent Functions