Solving a Quadratic by extracting square roots : 1.) If the Quadratic is in the form (ax + b)2 = c , write
3.) CHECK your answers.
Solving a Quadratic by Completing the Square: Before you begin, write your equation in the form ax2 + bx = c .
1.) Take the square root of the first term .
2.) Take the middle term divided by your answer from the Step 1.
3.) Take the answer from Step 2 and divide it by 2.
4.) Take the answer from Step 3 and square it.
5.) Add the answer from Step 4 to each side of the equation.
6.) Factor the left and simplify the right
NOTE: The left always factors as (#1+# 3)2 .
7.) Use the Extracting square roots method to solve .
8.) CHECK your answers.
Solving a Quadratic using the Quadratic Formula: 1.) Write your equation in the form ax2 + bx + c = 0.
2.) Use the Quadratc formula:
3.) CHECK your answers.
Likewise , when given |something| > a, this becomes two
something > a andsomething < -a
This becomes two problems:
-2x -3 > 7 and -2x - 3 <-7.
We can then solve each of these separately to get
x < -5 and x > 2. (Check to see if you get the same thing.)
Polynomial Inequalities : 1.) Get everything one one side and 0 on the other side.
3.) Set each factor equal to 0. The answers you get are your
4.) Set up test intervals using your Critical values to divide the
5.) Plug in test values to determine if each interval is positive or
6.) Choose the appropriate intervals for your original problem.
Rational Inequalities : 1.) Get everything one one side and 0 on the other side.
2.) Rewrite the non- zero side as a single fraction.
3.) Factor the top AND bottom of the fraction.
4.) Set each factor equal to 0. The answers you get are your
5.) Set up test intervals using your Critical values to divide the
6.) Plug in test values to determine if each interval is positive or
7.) Choose the appropriate intervals for your original problem.
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