Presentation on theme: "Equations in Quadratic Form The "u" Substitution Method."— Presentation transcript:
Equations in Quadratic Form The "u" Substitution Method
Before we solve the above equation, let's solve a quadratic equation that we know how to solve. Factor Set each factor = 0 and solve Let's use this to solve the original equation by letting u = x 2.
Factor Set each factor = 0 and solve Now that we've solved for u we have to re-substitute to get x back. Remember u = x 2 so let's substitute. If u = x 2 then square both sides and get u 2 = x 4. Substitute u and u 2 for x 2 and x 4. Solve for x by square-rooting both sides and don't forget the
Factor & set each factor = 0 and solve You can determine if an equation is of quadratic form where you can use the "u" substitution method if you call the middle variable and power u and then square it and get the first term's variable and power. So let u = z 1/4 and get u 2 = z 1/2. Substitute u and u 2 for z 1/4 and z 1/2. Solve for z by raising both sides to the 4 th power
Factor & set each factor = 0 and solve Let's try one more. Call the middle variable u and then square it to see if you get the first term's variable. So let u = x 3 and get u 2 = x 6. Substitute u and u 2 for x 3 and x 6. Solve for x by taking the cube root of both sides
Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephens School – Carramar