04-2a+-Properties+of+Quadratic+Functions+in+Standard+Form

//**Objective:**// We will write and graph quadratic functions in standard form and use the maximums and minimums to solve problems.

When we studied linear equations, we learned to write them in
 * slope-intercept form (y = mx + b),
 * point-slope form (y - y1 =m(x - x1 ) and
 * standard form (Ax + By = C).

Each of these forms has its value, and the best one to use depends on the circumstances. For example, if we want to graph a function, we write it in slope-intercept form, while standard form is most useful for solving systems of equations. There are several different ways to write quadratic functions as well; in this lesson we will examine the Standard Form of a Quadratic Equation, and learn how to utilize its properties in solving problems.

//**Axis of Symmetry**// When we drew the graphs of quadratic functions in the previous lesson, we noticed that the graph is a U-shaped curve called a parabola. We also may have notice that the graph of the parent function is symmetrical about the y-axis. Parabolas that have been translated are still symmetrical, but about a different vertical line. We call the line that the parabola is symmetrical about the axis of symmetry. The axis divides the parabola into two congruent halves. Here is a handy chart: 

What this chart tells us is the the equation of the line of symmetry passes through the point "h". Since the axis of symmetry is a vertical line, the equation of the axis of symmetry is x = h. Remember to be careful about the sign of h -- the negative sign belongs to the formula, so if you see x - h, the h is a positive number but if you see x + h, it is equivalent to x - (-h), so h is a negative number. The equation f(x) = a(x - h)<span style="font-family: Verdana,Geneva,sans-serif; font-size: 120%; vertical-align: super;">2 + k is in vertex form; more on this later.

<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%;">media type="file" key="Identifying the Axis of Symmetry1.swf" width="360" height="270" <span style="display: block; font-family: Verdana,Geneva,sans-serif; font-size: 120%;">Proceed to Standard Form of a Quadratic Function