OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: equation

So far we have been able to solve quadratic equations using the factoring method.

The idea was to set the equation to zero, factor it, then set each factor to zero and solve. The zero factor property allowed us to solve factorable quadratic equations.

Solve by Factoring Playlist

Solve by factoring.

At this point we will learn a new technique that works for quadratic equations that are in the following form:

The idea here is to isolate the x^2 term and then apply the square root property. For example, if

then it is fairly clear that x = -3 or x = 3 which can be gotten using the following property:

When applying the square root to both sides of an equation remember to include the + or -.

Solve by Extracting Roots Playlist

Solve by extracting roots:

Step 1: Isolate the square term.

Step 2: Apply the square root property.

Step 3: Be sure to include the + or - and solve as usual.

Compare the next three problems to the first three of this section, they are the same questions. Notice that the two very different techniques give us the same solutions.

Instructional Video: Solving Quadratic Equations Using Square Roots

Solve by extracting roots.

Solve.

Video Examples on YouTube:

Many of the problems that we will encounter in this section involve parallel or perpendicular lines. To study this we must focus on the slopes of the lines.

[ Interactive: Parallel Lines ]

Instructional Video: Parallel and Perpendicular Lines - Part 1

There is notation that corresponds to these ideas, for example,

reads "m perpendicular". To find the slope of the perpendicular line simply reciprocate the number and change the sign.

[ Interactive: Perpendicular Lines ]

Find the corresponding perpendicular slope.

Of course, just use the same slope if you are asked to find the slope a parallel line.

Are the lines parallel, perpendicular or neither?

Find the slope of the line perpendicular.

Now we use these facts and the formula for equations of lines to find equations given certain geometric information. Recall,

Example: Find the equation of the line perpendicular to y = −1/4 x + 2 passing through the point (−1,−5).

This three step process using slope-intercept form always works. We could find this equation using point-slope form as well as demonstrated below.

Example: Find the equation of the line perpendicular to y = −1/4 x + 2 passing through the point (−1, −5).